Chain width has nothing to do with strength. I rode 3/32 chains with no brakes for a year with zero problems. Many track racers even ride 3/32 because they are lighter. The only reason I switched to 1/8 was because it was hard to find 3/32 by 144 chainrings locally and because the fat chain just looks nicer. KMC makes a very good 3/32 chain. Businesscycles has them.

Regarding firs time brakeless. Make sure your drive train is tiptop and then just listen to your bicycle it will tell you how to ride you will feel what to do.