Yes, serial cables can have 9 pin or 25 pin connectors, DB9 or DB25. Right by your door on the machine where you insert the floppies should have a DB25. Search DB25 on the net and take a look at what you have and it should look the same. Trick will be to find a USB to DB25 direct cable, most likely you'll find DB9 to USB and then have to use an adapter from DB9 to DB25. But like Convertek said, best to contact Sporty Bob and get a cable from him, I'm sure he's already figured out which cable combinations do and don't work.
I've been doing this long enough that we used to make all of our cables "back in the day". So now, I just buy DB9 or DB25 to RJ45 adapters for each end and then I run CAT6 network cable between them. But you have to play with the wiring on the pins to get them to work, kind of hit and miss but I figured it out. In your case, probably best to buy a cable that is promised to work with your combination.