I doubt they will catch foot rot, your bigger concern is the concentration of bacteria and the potential for it to take up residence in or on your pigs.
During lambing we use a disinfectant on the floor of the pens between sheep, this is to keep down the concentration of germs and prevent lambs from dying.
Your idea is not something I would consider, you will probably be ok, but the risk involved with the potential transfer of germs and spread of harmful micro-organisms outweighs the limited benefit and may be very costly in the longer term.