I know they do have Karaoke a few nights, so its possible there is some "open-mic" time that evening. You can always ask the cruise director or who ever is in charge that night, they may just let you do it, enjoy!
I just got home from the Voyager... (What a ship, What a vacation) Yes, they have Karaoke for several nights. They have about three or four nights of qualifiying. (this takes place in Cleopatra's needle) They pick the best female, male, and deuet from each night, then on Sat. night they have all the winners back to the main theater for a contest.
They also have a talent show. So, If stand up comedy is your talent, go for it. They will have sign ups for the talent show on Monday.
The last few cruises I noticed in their ads for people to try out for the passenger talent show, they were not allowing comedians. Don't know if this will apply on your sailing, but I'd check with the CD when you board if you want to pursue this.