Signing the mat isn't a good idea because, after all, just remove the mat and the signature is gone. Put on a new mat with a different signature, and then what?

For drymounted prints a classic presentation is to bleed trip the print and tissue, mount on the board, then cut an overmat larger than the image area. Then sign the board just below the image. In the same way, if you don't want to bleed trim, or just don't want to see any handwriting, sign the back of the mat board behind the image. If art fair judges don't like it, please take my word for it that high end galleries tend to dismiss out of hand as "amateur" any work presented with a signature on the mat. You need a real good reason to insist on swimming upstream against this convention.