I've seen a combat run as a skill challenge before, and it worked quite well. I'm wondering, though, if anyone has made more formal rules for a combat skill challenge, beyond "pick main skills and set DCs", particularly when it comes to incorporating powers, HP, and healing surges.
[RPG] Combat Skill Challenges
combatdnd-4eskill-challenge
Related Solutions
The magic item you're thinking of is probably the Potion of Regeneration. The level 9 version costs 160 GP a pop and gives you regeneration 5 while you're bloodied. It also costs a healing surge, which might be a problem for your wizard if you do a lot of encounters in a typical day.
Trollhide Bracers have a daily that also gives you regeneration 5, not just while you're bloodied, but those are a level 19 item so it'll be a while before you might have those.
Armor of Sudden Recovery is great for regeneration. You can, as a daily, convert any ongoing damage you're taking to regeneration -- so if you're taking ongoing 10, you can turn it into regeneration 10. I would strongly recommend a set. A slightly cheesy but amusing option: combine that with Dragonfire Tar, an alchemical consumable which does ongoing damage on the target. Use that on yourself. Check with your GM before using this one, though.
Back to non-cheese. For your neck slot, an Amulet of False Life has a daily that gives you temp hit points equal to your healing surge value. That's effectively an extra second wind once per day. I think that's better than the Amulet of Life, which allows you to spend an extra surge once per day when you spend a surge, since you have to wait for someone to heal you or use second wind with the Amulet of Life.
Diamond Cincture is another effective second wind, once per day. So that's pretty good. It fills your waist slot.
OK, let's see. Strategies -- don't forget about Shield. That's a very good defensive utility. With any luck it'll prevent one hit per encounter. For your level 10 utilities, you have a few interesting choices. Mass Resistance is a life saver if you're fighting anything at all elemental. It's party-oriented, which is nice. Blur is a great power to protect you -- you can't be seen by enemies more than five squares away, plus you get some defensive bonuses. If you have some way to fly, which you probably will eventually, this is a great way to stay safe in the air.
No, 4e does not have any non-racial ability boosts in the Heroic Tier.
Fourth Edition's ability requirements for feats (and its assumptions about the level of your basic stats throughout the game) are much more stringent and coordinated than in 3.x, and ability stat bonus are not part of regular character progression until level 21.
You should not be concerned about all of your stats being good.
With the typical 4e 22-point array, you can get one score up to 20 after racial modifiers, at the expense of secondary stats. This works for some classes and builds better than it does for others, who might prefer to have two 18s over a 20 and one 18 (again, after racial modifiers, assuming optimal choices in that field).
As you can see, it is not expected --or possible-- to have three really good stats. At best you can get two good and one okay stat. 4e's defenses each use the better of two stats (Str/Con, Dex/Int, Wis/Cha), so there's rarely any mechanical advantage to being concerned about more than three stats. This is also why most classes have either one attack stat and two options for secondary stats (called A classes), or two options for attack stat and one secondary stat (called V classes): they expect you to only focus on two or maybe three stats, and have accounted for this in the game's design. (There are even utility powers which let you use one stat in place of another, or one skill in place of another, once per encounter in non-combat situations like skill checks.)
Discussion of your situation
A fey pact Hexblade should be stacking Charisma first (your main attack and damage stat) and Dexterity second (the stat associated with your pact's riders). Constitution is an alternate secondary stat for Hexblades, but usually associated with other pacts than the fey one. As you're discovering, 4e point buy is designed so you can't stack many stats especially high; it's part of the game balance.
Suggestions
First, it's usually a mechanically poor choice to have a race without a bonus to your attack stat. This is even more true when you want two secondary stats. Without changing your race, the best you can hope for is Cha 18 and 15s in Dex and Con. This isn't shabby, for the record. You shouldn't feel like it's a bad set of stats; given that your choice of race is not ideally suited to your class choices it's quite respectable.
If you choose a race with +Cha and +(Con or Dex), then you can get an 18 in Cha and 18/12 or 16/14 in Con and Dex.
If your primary concern is that you prefer Con-based warlock powers and want more durability, then switch to a Hexblade pact that uses Con for riders: Elemental and Infernal both enjoy them, letting you relegate Dex to a tertiary stat that is mostly for skills but might also come up as the occasional power rider.
Alternately, you could be a regular warlock with a Con-based pact. It's possible for Infernal, Sorcerer-King, Star and Vestige pact warlocks --but not Hexblades of any type-- to use Constitution for their attacks. This makes Charisma a secondary stat letting you focus put more points into one of your preferred stats without feeling like you're nerfing your attacks. However this also removes Dex as a stat your class is concerned with at all.
If you're more concerned with stacking Dex, then keep your current build and don't worry as much about Con. There are great Cha-based lock powers, they just have different playstyle assumptions. If you honestly like the Con ones so much, look at my suggestions above because feylock isn't going to make you happy. If your major concern about Con is survival, then look at the Cha-based powers which provide some powerful avoidance and control as alternate survival-enhancement options. @Waxeagle's suggestion to consider the Born Under a Bad Sign / Auspicious Birth character backgrounds is good also; it lets you use an alternate ability to determine starting hp (but not your healing surges).
Best Answer
I've seen combat skill challenges for things like riots and obligatory thug attacks. Any skill was usable as long as we could come up with a description of how we might use it.
For example, a riot breaks out in the marketplace the players must put down the riot and keep the innocents safe. Heal was used to tend the wounded, insight to gauge the intent or morale of the rioters, subduing the rioters called for athletics, endurance, or intimidate rolls. Etc... A failed roll usually cost a healing surge from being beaten by the rioters.
Sometimes, a well timed or very suitable power could gain a automatic success. But it had to be a really creative and effective application of said power. Usually powers would provide a circumstance bonus to a skill check.
I've never seen anyone track hp or healing powers in a skill challenge. I guess because you might as well run a full combat then. The healing surge penalties for failed checks usually seems to be sufficient to capture the consequences of a fight.
Failing the skill challenge sometimes has additional consequences, such as capture, etc. But death seems too severe a penalty. If it's a tough enough fight to kill a PC then I think it would be better run as a combat.