Schwinn varsity and alloy wheels
 

I picked up a really nice wheelset for the green monster ( as I call it now) complete quick change and a new freewheel gear set. PROBLEM they don't fit. The forks and dropout of the bike are too narrow to fit the wheels. Is it possible to change the wheels to the right dimension by removing the quickchange and going with the bolt on axle or should I just bag it and take them back to the seller?

I'm no expert on Schwinn Varsity's. But, if I have an older bike I like and intend to keep, I look for a nice set of alloy wheels/rims with hooked bead because it does make a difference in the braking and ride. The hooked bead allows for the use of higher pressure tires, which I like to ride. IMHO, I think its easier to maintain rim tru with an alloy rim, but that's just my opinion.
So, if it were me, I'd modify the quick release axles or mount the old solid axles and try to make the alloy rims work.

If you are referring to the actual thickness of the dropouts, why not put a washer or two on each side of the axles (under the locknuts) to take up some space? Just be sure to do the same thing to both sides to maintain wheel dish.

No the dropouts and the forks are too narrow the dropouts and the forks need more spacing to allow the axles to fit in the slots

I think I can chuck the locking nuts in a lathe and face them off probably about half the thickness of each one and maybe the cone nuts too. Nice to be able to have access to a machine shop full of mills and lathes then I can cold set the frame per Sheldon Brown and I should be duck soup. Will let you know how it works. Wish I knew how to post pictures to show the finished job.