That error message suggests there may be a hardware issue with the floppy drives. This could be:
Bad floppy diskette itself, which could be as simple as unformatted or as "complicated" as faulty disk media. Use a diskette that you know works for other files.
Bad drive, which could be either drive. Be sure the drives are working by testing file copying from other diskettes with other files.
Incompatible drives - This is a long shot, but is the newer WinME drive high density while the older Win95 drive is low density? If so, you need to use a low density diskette and force the WinME drive to use the low density format, because the old low density drive can't read a high density diskette.
Finally, have you considered learning enough about networking and setting up the proper protocols in the operating systems so that you don't have to use the wizard disk? There really isn't much rocket science going on behind the scenes of that wizard. If a computer has never had any networking hardware installed, there are a few tweaks to the My Network Places (on ME, was called Network Neighborhood on 98 and 95) properties, but nothing wild going on in there like with installing hardware drivers... Just something to consider.