I believe Firewire wasn't introduced until the G3 Mac, and quite certain it's not available on your 6500 (I have a 7600 and it's definitely not on that machine).
The only other option I can think of would be an ethernet connection between the two machines (preferably with a router/switch in-between, otherwise you'll need to find an ethernet crossover cable), but without a monitor on your 6500, it would be near impossible to configure. You might have to borrow a monitor to facilitate this.
The 6500 (I believe) also used SCSI hard drives, so pulling the drive and sticking it in an external case isn't really much of an option either. I was lucky in that I had an external SCSI CD burner available when I decommissioned my 7600 a few years ago and was able to not only burn the files on my hard drive, but also compiling my old 3.5" floppies onto a CDR.
Perhaps someone else could have better advice...