I personally don't like snapping the lid down at all for the same reason you stated earlier. It's a pain to get it undone and if you're not careful that can lead to a mess. I've always used a linen dishcloth, which used to be white but is now tie-died. Ilay over the top and tie on with a piece of cord.
The main point being made here by everyone is spot on. During fermentation, the wine needs OXYGEN. The more the merrier. Actually, it's the yeast that needs it, not the wine. Anyway once you reach a S.G. below 1.020 you can rack it into a secondary to finish it off. Personally I usually go with 1.010 before I rack. If you don't have a secondary then I guess snapping the lid on and fixing an airlock would be your only option.
The only reason to cover your wine at this stage is to keep out any nasties that might get in there. Although I have children I haven't had to deal with cookies, but legos or My Little Ponieswouldn't be out of the question. The kids need to be kept away with a locked door in my opinion. You're main concern is dust, pet dander and insects, especially fruit flies.