You should not neglect the healing and follow up care of his wound. Talk to the hospital, they often have specialized people who will work out a payment plan with people in need of financial help. Sometimes hospital will just pay for the bill, but talk to them and don't neglect bills as they will hurt your credit and future needs for care.
As for his wound, the dressing should be changed at least once a day with clean, unused roll gauze, and the skin should be checked for signs of infection (redness, heat, pain, swelling or pus leaking from the wound) A local topical antibiotic like Bacitracin or Neosporin should be applied twice a day. If he still has stitches then a surgeon should remove them as this service is included in the price of the surgery. His hand should be elevated if swollen. If all goes well, his care really won't be that much, as his body will do most of the work.
Good Luck