I would'nt call it a sin, unless the paint was in really nice condition, There seem to be alot of Schwinns around so you won't be destroying a rare paint job. You will lose some character, I have had a hard time locating Schwinn decals in the past, and the factory paint is probably more durable. That said the Schwinns I have are armored tanks and I think they will be around for the next generations childrens children. I see I am just across town from you, You don't see many people from around here on the forums. If you don't mind a little cost, I think powder coating is a good option, there is a guy in Akron who does bike frames for $80.00, and you will have at least 30 invested in spraypaint, sandpaper, etc. Have any pictures of your Varsity?
-Matt