As you observed, you can't trigger Underhanded in combat on its own
You are 100 percent correct that since they can only take a Standard or a Move action RAW (free actions are also allowed). At best the drawing of a hidden weapon can be made to be a move action (but you still only get 1 or the other) utilizing the Quick Draw Feat.
Bandit's can easily make use of underhanded
The rogue Bandit archetype gains Ambush(Ex) at the cost of Uncanny Dodge.
Ambush (Ex)
At 4th level, a bandit becomes fully practiced in the art of ambushing. When she acts in the surprise round, she can take a move action, standard action, and swift action during the surprise round, not just a move or standard action.
Thus the player would be able to (with Quick Draw) pull the weapon out with their move and still have a standard to attack the enemy with.
The Betrayer Feat might apply
Benefit: When you succeed at a Diplomacy check to change a creature’s attitude, you can draw a weapon and make a single melee attack against that creature as an immediate action. If you changed your target’s attitude to friendly or better, your target is considered flat-footed against this attack. If the target survives, it takes a –2 penalty on its initiative check for this combat. Once you attack a creature, its attitude becomes hostile.
However the wording seems to imply that combat begins after the betrayer attack, but then again Surprise is worded extremely vaguely (at your DM discretion).
Surprise
When a combat starts, if you are not aware of your opponents and they are aware of you, you're surprised.
Ostensibly the target of the Betrayer attack knew the other person was there, but not as a combatant and as a DM I would allow the attack to be treated as a Surprise round attack.
Possible workaround through items
My Pathfinder knowledge is insufficient to know if this is really RAW, but both the Sword Cane and the Switchblade can be drawn as a swift action. Whether this still applies when the weapon is hidden is something I'm not able to divine. Some people on Paizo's forums seem to think its workable and others don't.
While a character that first takes one or more levels in the class gunslinger (or another class that gains the character the class feature grit) is prohibited from taking the feat Amateur Gunslinger, such a character is not prohibited from taking the rogue talent grit. The character won't meet the prerequisite for the feat Amateur Gunslinger that comes from the rogue talent grit, but the character still gets the additional grit feat from the rogue talent.
Note that such a character would still have the feat Amateur Gunslinger, but the character won't realize any of that feat's benefits, and because the feat's source allows no other choices beyond that feat, the feat Amateur Gunslinger isn't eligible for retraining.
If, still later, such character gained another level in a class that granted the class feature grit (like an additional level of gunslinger), the character could immediately trade the feat Amateur Gunslinger for the feat Extra Grit. (This is strictly according to the rules as written. A kind GM may allow a character who already has the class feature grit who takes the rogue talent grit to immediately swap out the feat Amateur Gunslinger for the feat Extra Grit without mandating the character to take another level of, for example, gunslinger.)
Best Answer
Talk to the GM about the action needed to designate prey
The rogue advanced talent hunter's surprise as its Benefit says
Unfortunately, no action is listed for designating prey. Because it's an extraordinary ability, according to Actions in Combat designating prey takes a standard action to employ, but there is some debate. So far, the only answer seems to be to ask the GM.
However, the second part is clearer. The teamwork feat Swing About as its Benefit says
Note that, because of the way teamwork feats work, in addition to the party member doing the swinging, the rogue himself needs the teamwork feats Swing About and the feat Escape Route, the feat Swing About's prerequisite, but, if the rogue has all that, once per day (as per hunter's surprise) this could be done.
That's an awful lot of resources to devote to that one thing, though. And if you're going that far, be sure to get a weapon with the magic weapon special ability sneaky. (About which there's also some debate.)