hmmm...i think kayce believes you want to go fixed gear, which can also be considered fixed gear.

however, I believe you want to go to just singlespeed which in that case you can keep your original wheelset, and just take a freewheel tool and take off the 5speed cassette and thread on a single speed freewheel.

you might not even have to redish the wheel, i have done a number of single speed conversions and have gotten pretty good chainline without redishing.

but if i were you i would still purchase a 700C wheelset, a nice pair can be had for around 100 from velomine.com and you can still preserve that vintage look and now have to compromise with steel rims.

also, the schwinn le tour is an excellent bike, 4130 chromoly. mid-end road bike form schwinn...if i found one in good condition, i would def keep it.