If dropping the bucks for a new box that drops the key is not possible, you might try this -- it's worked for me and produced some interesting "original" results:
If you can find the lower harmony to the melody, give that a shot. You'd be surprised at what a new twist it can give to an old standard.
Another thing you can try is to play the song in the other position on the accordion. Many, many songs will work perfectly fine especially if it is just to cover a request. Here is one that I have done several times: Ivy Dugas recorded "The Gravel Road" in Bb on a Bb. Even in Bb, it is a pretty high song. I don't have a Bb, so if someone requests it, I play it in A on a D accordion. There are a few subtle differences in the melody, but you can get your point across.