You are being very optimistic if you think you can put on a decent stage show in just 11 days, without ever having done anything stage related before.
Stage magic is not only about the actual trick, but mainly about how you speak, how you script your act, how you compose yourself, how you manipulate your area, how you use your props... completely different than close-up.
Do you not agree that we owe it to our audiences - people who are giving us all their attention, to give them the best damn show that we can? If you don't agree, then by all means, do this show, do an arm gag, and learn a gimmicked drawing duplication...
The wise decision here would be to pass up this opportunity and work on something for stage - something really really good. Then, hit 'em with all you got next year, or whenever the next talent show comes around.
Remember, even something as simple as the invisible deck can be done really well on stage, if you have a great presentation to it.
If you really want to do this show though, and learn a trick in just 11 days, just do the vanishing banana trick, and accept mediocrity - no patter or thinking on your end is really required from that, and I'm sure it'll fit your 10 minute requirement.
Good luck. Let us know what you decide and what happens.
-GJ