If you know the schedule of the child ahead of time, you can write the officials of your tournament and see if it possible to work his absence around the skit presentation. Like ask for a very early or very late skit time. They may not be able to accommodate you, but it would be worth asking. Somebody has to go last right?
You can make him director of the play, or the sign holder, someone who says the name of the play, flips the board at the end that says "that's all folks" (or whatever.:) You can make him a human prop in the play- coat rack with ultrasonic coat gripper anyone?-, which can be pretty funny, but also set aside in the event he can not be there.
More trying - and very dependent on the age of the students- is making the child the least number of the lines in the play his understudy, so in the event he can not be there, the understudy says both sets of lines, not just his/her own. We've had years where this was not a good option, and years where the kids stepped in for people who were absent during the practice and I thought,"Great. if one person is absent for illness, this will still be ok!"