Rules as written: the subtleties of "can see" you're reading into don't exist. Whether you "can see" something mechanically means "you have line of sight to it." This heavily implied by the Player's Handbook, and finally made explicit in the Rules Compendium's section of Line of Sight on p106:
A few powers do require a user to be able to see a creature to target it, however. For instance, a power might specify that it targets "one creature you can see." In other words, the creature must be within the user's line of sight.
So the Warlock's curse simply refers to those enemies to which you have line of sight. You have line of sight to someone simply if you can trace the corners of your square to the corners of their square, and that's it, so whether you're covering your eyes doesn't change anything. Since covering your eyes doesn't change your line of sight, the only RAW answer is: nice work, smart guy — you still have line of sight to all the other monsters.
The rules are built on the assumption your characters are generally trying to look around and be aware of their surroundings, and not pulling these tricks. If it doesn't make sense why you can't use a spyglass to affect who you can see and change your line of sight, it's because you've exited rules territory, and at that point the rules aren't expected to make sense.
The RAW way to eliminate line of sight is to manoeuvre around obstacles and eliminate it. So that's what a Warlock wants to do, if they want to get creative with limiting their Curse targets by vision.
How can this make sense or be explained in interpretation or story?
Before this, there's a big principle of D&D 4e to understand: it prioritises balance and fun mechanics above rules making total sense story-wise. Thus the mechanics do not bend or adjust to what makes sense simulation-wise: powers and features do what they say, and it's up to the story to make sense of that. There is no attempt to simulate things realistically, which is a major point of contrast to previous editions, and a contributor to D&D 4e dismantling the Omnipotent Wizardry Tier of classes.
So, given this 4e ethos, the axiom is that Warlocks can only curse the nearest enemy in line of sight (whether the Warlock's covering an eye or not). As BESW points out, this is a fun and interesting part of the Warlock's tactical decisions. It's up to the Warlock's player and their companions to make sense of why this is the case, which could be a pretty fun opportunity to flavour your Warlock or their magic.
- It may be the nature of the curse. It refuses to be cast any other way, or picks its own target.
- The Warlock may be capable of casting it another way, but have good reason not to. Doing so may lead to very, very bad juju. Doing so might be violating their pact.
How would I handle someone trying to do this?
How we'd handle it in our own games is a matter of opinion and style. Some would allow it (especially if they're a fan of rule-of-cool and it was cool). Others would ask the Warlock to put the telescope away. I'd probably do the latter, so as to not have the small headaches that might follow from wandering outside the rules into simulationist territory.
It is a fun feature for a Warlock to deal with (having played one myself), and truthfully, having read how BESW would approach this, I'd do as he does.
Don't run the campaign
It is often important (but not always) for the party to have a preexisting, long term reason to stay a party. It is especially important in situations like this, with non-standard parties. Unless that reason is part of your pitch, it is incumbent upon the players to come up with that reason.
Your Options
Make it a One-Shot
So you don't lose a game session you can run the game as is, without a real reason for the party to stick together, until the party inevitably falls apart. This kind of play is usually lighter in tone. The party may actually come up with a background in this throwaway setting.
Have them Re-Roll
You can have them come up with new, more standard, characters for the game and continue as planned.
Go Bowling
Just don't run a game at all. This leaves you open to come up with a new campaign idea, or revisit this one later when the players are willing to collaborate on party design.
Best Answer
I think the key question is: are you planning for each "half" of this combo to take separate actions? (As in, Hodor does X, and then Brandon does Y).
If no, then I'd be inclined to handwave it as fluff. (This human is actually two halflings in a trenchcoat). Mechanically, you're A Character, and the weirdness is flavor. The only caveat I'd have is that if the two are separated, one goes to NPC-status (or just is handwaved away, like most mounts). You're one player, you get one character.
If yes (either because you want each of them "doing" something, or you want the flexibility if they're separated), then you're a lot more restricted. 4E is not kind to familiars and companions (probably because they got abused a bit in 3/3.5). So, other options:
Will your GM let you flat-out play two characters? Some will (esp. if they like the character concept), and that gives you two mechanically usable players, no problems required. (Alternatively, you could try and talk another player into taking half of the "combo")
Mounts and pets are an option with skinning, but I think what might describe your situation better is just a plain hireling (or follower at a high enough level). Play the little guy, hire a big guy to carry you around.