One of the screws holding the plastic chain cover wiggled off, and of course HD has no suitible sized replacement (I think it's a short #12 but HD stocks about 2 #12's all of which are around 2" long). Not sure where to find a suitible replacment, but until then how bad is it to ride without it? Am I going to get dirty chain lube gunk everywhere?

YES!!! you will get chain lube everywhere!!! I did this and immediately found a chain guard the next day. I went to lowes and got a short bolt and nut. Not sure the size, but I will look when I get home. Zip tie it if you have to.

Zip tie is a good idea...

I gotta find a better place to get screws and bolts. The selection at home depot really sucks.

If you have an ACE hardware they seem to have a good selection 

If you can't find a decent hardware store with a screw short enough, buy the longer one, and a nut to go with it. Put the nut on, all the way to the head, and cut the screw to the proper length. When you take the nut off, you'll repair the threads, and have a screw of the proper length.

Zip tie! My Chain guard has been zip tied in the front since the bike was new.. .I've been too lazy to get a new bolt... IMO zip ties add character....