Is there a tool that will help me construct a list of games with a more specific game mechanic?
How important is this to you? Is this something you are simply curious in? Or is this something you want to put real effort and time into accomplishing for a task or job of some kind?

If it is just a hobby, you could go to your local game stores with a notebook and ask the people there, look at the games there. Repeat at a few other game stores and you should have a nice list. (similar to just browsing games on BGG)

If it is something you want to do more seriously. You could try to contact some of the big board game manufacturers (like Fantasy Flight for instance) And directly ask them which games use non standard N-sided dice.