When I had SA non nappers, I had a quiet time schedule of silent reading for 30 minutes, educational computer games for 20 minutes, and then I sent them outside. I made sure everyone used the bathroom right after lunch and made it clear that was it until QT was done
I have water bottles for each child that I fill up and put out on the picnic table. I found I couldn't send them out the entire time because they would get bored and it would be back and forth. By breaking it into chunks it was manageable.
That said, this is exactly why I don't take non napping kids. I set up my nap room so that kids can't see each other and have a couple loud white noise fans going so they can't hear each other. They don't have to sleep but all my kiddos (even my two 5 yo's) take a rest. I find that until they go to school, they can't seem to handle the independent quiet play I require for QT.