Back when I was a Mac technician I used to gloat to my PC technician friends about how I could go to any Mac site with just an external scsi drive and a few cables. They used to have a second briefcase just for boot floppies and installer floppy sets.
Surely these days there's nothing that doesn't work with a USB 1.1 thumbdrive? Of course some organisations lock down the system so you can't use removable mass storage (and floppies are certainly not mass anything).
If you really only have access to a floppy drive, you could try something like the Sandisk Smartmedia Reader Flashpath Floppy Adapter or the Sony Memory Stick 3.5" flopppy adapter and get access to larger storage via a floppy drive. I would imagine that performance should be at least no slower than a regular floppy.