Game bags and/or cheesecloth won't keep the outside of the meat from drying out. The only time I use bags is to keep flies or bees off the meat. Just skin away the dry layer like you did, helps to get rid of the muscle fascia so it's not a big deal.
Remember, life begins at 40! If it's below 40 degrees you can hang meat a long time without worry. If it's warmer than that be a little more cautious. If it's a constant 60 degrees, you can hang meat for three days and then it needs to be in the freezer.