Those wheels would look pretty odd on an old schwinn. You'd probably want something more like these: http://harriscyclery.net/itemdetails.cfm?ID=701 or these: http://harriscyclery.net/itemdetails.cfm?ID=2606, or these: http://harriscyclery.net/itemdetails.cfm?ID=3135

They're less expensive too.

If you wanted to convert to 700c it would probably work, if your brakes can reach the rims. 700c is slightly smaller than the 27" you have now. If you don't want to have to worry about that, a new 27" wheelset like one of the 3 above would work fine.