I got given 2 sets of generic interchangeable punches, 1 border set and 1 small shapes set. Both the punch lever things have been broken but the punches themselves still work great.
What is the best way to use these now? The shapes have a small circle punch button, and the borders a longer one.

Not sure I know which punches you're talking about. Are they sold here in the store so you can link them to this thread?

These are ones from a department store, no brand and a few years old. Just wonder if there was like a universal handle available?

If they're that obscure that they don't even have a brand, then no, you're probably not going to find any universal handle. I can't imagine what they look like from the description. Can you post a pic?