Continuing in my survey of methods and options for old school resolutions of different challenges. Today, the challenges addressed by the skills "Disguise" and "Escape Artist." Disguise
Disguise is treated as an "opposed check" in games from 3E onward, meaning that the character's roll is set off against a die roll by the person who might see through the disguise. In older games, the only place this shows up as a "rule" is for the assassin class. Much like climbing and the thief class, it's definitely true that SOME sort of resolution is needed for regular old people making a less-professional attempt at the art.
I generally use this as a flat percentage chance (or a # in 6) to succeed, based on the situation. After all, disguises from a game point of view (a) aren't a trained skill, so nothing about a class or level (other than for assassins) really suggests that level would be a factor, (b) aren't obviously tied to any specific attribute other than slightly to charisma, and (c) don't have an offsetting role-playing component unless the disguise fails, which isn't the issue here.
So in general, I recommend using a base chance, picking the likelihood based on the situation.
Try using a check against the character's dexterity (3 or 4d6 if you use a bell curve, d20 if you use a linear chance). Either give a thief an advantage, pose a thiefly solution (you can pick the lock on the cuffs, but at a disadvantage), or allow the thief a dex check when no one else gets one. It's perfectly okay to just say that it's not possible to escape at this time.