Just use the nointro romsets off archive.org. About as close as you can get to dumping the cartridges yourself.

Because the programs are going to be run in an emulator, it would be safe

Yes, technically, some game ROM could be coded to exploit some emulator zeroday but because the market is tiny it seems very unlikely

I've been using it for years and never encountered any issues (besides the fact that they've removed comments from the download pages).

What game?