I have run tires about that wide on balloon bikes, the trouble is one manufacturer's definition of "2.35" might be different than another's. The rim width also plays into it.
For what it's worth, those look to be Fat Franks, and I have seen gobs of pictures of old Schwinn ballooners on this site with those tires. Probably without fenders or with stock fenders, I don't quite recall. Sometimes aftermarket (Wald) fenders hit when real Schwinn ones wouldn't. Do you have fenders? I also see a sheave on one of your wheels for a Whizzer or something. Will the tire hit the belt? I don't know. You are probably just going to have to try it.
Be sure to true up your rims. Getting oversize tires on a bike is usually possible, but the rims need to be straight.