Shouldn't be a problem.
Format a 720k disk in your PC on the A600 using Cross-DOS. Save your transwrite file onto the floppy and carry it upstairs when needed.
Make sure you format the disk as 720k as the Amiga 600 won't accept HighDensity floppies.
Or, you could run a very long serial or parrelel cable and link the 2 computers together, but that's probably more expense/effort than is needed.
Back up important stuff regularly as modern floppies are rubbish.
