Go find a set of the Barton tapes. This is a series of shows John Barton, at the time the dramaturge for the RSC, did for British television about performing Shakespeare. He gets a staggering collection of British actors to help him out, including such luminaries as Ian McKellen and Patrick Stewart (the cast rotates from show to show). (There’s an associated book that’s basically just a transcript of the shows.) And in one of the early episodes, they do dramatic interpretations of various sonnets. IIRC, one of the actors who participates in this bit is David Suchet, probably best known in the U.S. for playing Hercule Poirot.
I’m recommending you do that, rather than trying to suggest a specific sonnet, because really you can pick any sonnet and make it work by applying some imagination. But that’s the thing; sonnets are not (and were not intended as) drama: They require a lot of interpretation and imposition on the part of the actor to function as anything but pure poetry. You have to pick a character and a situation, and invent a narrative context, in order to perform a sonnet as drama, and the Barton show will give you some guidance in this.
To give you an example from my own experience, we did this in my classical-text group (I have an acting degree). I chose the sonnet that begins, “That you were once unkind befriends me now” (full text), and I invented a scenario in which I was sitting next to somebody in their hospital deathbed rationalizing my decision to cut off their life support. Melodramatic, yes, but it worked reasonably well.
The choice of using sonnets as audition pieces strikes me as being awfully peculiar, but if you can find the Barton tape you’ll have a leg up on the competition. Check the biggest local library to see if they’ve got the series.
Actually, I just changed my mind, sort of. I still think you should go find the Barton tape(s), but if you want to do a “funny” sonnet that will compare well to As You Like It, use number 135. In reading it, be aware that “will” is a triple entendre: It’s Shakespeare’s own name, and it obviously means conscious effort or design, but it also refers to sex, both desire and the actual naughty bits both male and female. It’s kind of an obvious choice, and somebody else may be using it, but it’s probably the best alternative for the situation. Maybe you can pretend to be the expert and dole out sonnets to your competition so you know nobody else is using this one. 