AFAIK, you can, but it probably won't fit on single floppy. use LHA to compress it and split it on 880Kb pieces (IIRC it can split). You do have bootable floppy with for eg. hdinsttools, right? then just copy some basic commands to that floppy like LHA, copy, dir.
try everything before removing old HDD..
when using Lha, set these switches
-a -r -e -x -wsys:
and the one for splitting, cant remember it..