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It's always hard to make such judgements without pictures. That said, it sounds likes the best route would be to simply leave the paint or touch it up. I would almost certainly avoid repainting it completely. It's a lot of work, and will decrease value--and Schwinn Continentals aren't too valuable to start. Schwinn's quality of paint was generally very good, so it should shine again with a little polish such as Meguire's ScratchX or similar.

There are Schwinn Continental decals on ebay. Velocals is a popular decal vendor, but I don't see any Continental decals on their site. Cyclomondo (ebay seller based in Australia) is another reputable source for decals.

Complete Schwinn White Continental Bicycle Decal Set | eBay