I'm not sure if they'd even fit unless you got some 26x1"tires. If you're determined to stay single speed, probably the best fit would be to get the wheels from a Schwinn 10 speed and just put a single speed freewheel on it. You might want to adjust the spokes so it sits in the center like it should. Since you've already got caliper brakes, though, it would be quite simple to take the wheels from a 3 speed, like a Breeze or a Racer. Come to think of it, why not just leave the 5 speed freewheel on the ten speed wheel and put a derailer on it, too?
I should keep this to myself, but I have some ancient fixed gear racing wheels from a 1928 Raleigh Golden Arrow that would be a direct fit and lots of fun. I'd want some money for them, though.