Avery produces a lot of craft supplies, including 8 1/2 x 11 stickers that can be run through an inkjet printer, and then cut down to size. I only see white listed on their website, but would be surprised if they (or somebody else) didn't produce a clear.
One other idea may be to accentuate/clean up the border rather than try to hide it. For example, you could find a picture frame the size of whatever sign you made (say one to hold a wallet-size print) and use that to hide the edges.
Some people get the placards made up at trophy shops... may cost a bit more, but most I've seen look good and there are certain affects that are otherwise difficult to create.