|"Gee, I never heard of WIN95A--not sure what version I have."|
You can determine which version by following the directions here (under the "more information" tab):
Again (and trying to clarify what's been said already), trying to install a USB card into the Windows'95 machine (aka CTX machine) would likely be of little help, due to the pitiful support Win95(B&C) had for USB.
"Span-zipping" (similar to a floppy backup) would also be an option, but again, involves the use of floppies (perhaps a great deal of them) and would fail if any of the files aren't written properly from the old machine or read properly on the new machine (assuming the new machine even has a floppy drive).
Networking the machines could also work, but (unless using crossover cables) would involve purchasing a router (and network card for the CTX machine if it doesn't have it---and don't even think wireless router/card here), and configuring the network and permissions on each of the machines to allow file transfers.
Cabling two systems together is "doable", but would be dependent on the interfaces available to each machine. And although (as wizard-fred mentioned) parallel-to-USB cables exist, they're exclusively for printers. I've also connected two systems together with modems, but that's likely not an option you want to pursue.
Installing a CD-writer to the CTX machine would be a slightly better option, but finding CD-writing software for Win'95 would also be difficult (though I'm sure there's something out there). Plus, this would be a "one-shot" purchase, unless you have another machine to put the CD-writer into.
Removing the hard-drive from the Win95 machine and connecting to a newer machine that already has USB with something like this (OtH's link):
would give you the most likely success to recover the files too big for floppies. Whichever method you decide on (and assuming these files/photos are important) once you've moved them, back them up to something more durable (CD/DVD media).
"Channeling the spirit of jboy..."