Maybe you could fashion a leather belt for it if the inside of an abrasive belt doesn't work. Just make a long strip of 3-4 oz leather and glue it to an old abrasive belt.
I can't say any specific tools improved my working. That said, Any good quality tool does make your work better. Don't get cheap ones, you'll just wind up replacing them in the long run.
I like knives better for skiving than special purpose tools. In the photo, all but the middle general purpose knife work great, depending on the type of skiving I'm doing.
I use my drill press for my maker's stamps and other large stamps. Using it for punches is a good idea. I've thought about putting hole punches in it but haven't as of yet. Looks like it's a good use for your purposes. Good thinking.