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.
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).
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.