EDIT: Brian, I just noticed you are a guy.
Now relax and think of a sewing machine as a POWER TOOL.
If you don't own one, you can get a good basic Jenome machine for $100-$150...
They have a tiny one for $45, but it isn't good on heavy fabrics.
Elastic exposed to sun for five years becomes stretched out fabric. The sun doesn't do the little plastic parts a whole lot of good either.
Simple, well no. It's not complex, but it is Tedious.
Get a very good seam ripper and attack the curtains from the back ripping out the zig-zag stitching that attaches the elastic to the curtains.
You could painstakingly replace the elastic with 3/8 inch stuff from any fabric shop, but as I mentioned earlier the plastic may also be brittle. I'd rather spend the bucks to replace the whole hook assembly than to put in new elastic and have the hooks start to give out a year or so later. Putting the new hooks (or elastic) in is simply a matter of getting a good thread color match to the drapes, and sewing them in with a narrowish zig zag stitch.
Now is also the time to take a long hard look at the draperies themselves. If you don't like the color or they are getting ratty.... (Oh good heavens... next thing I'll be advocating is that the whole Airstream might be showing excessive wear and should be traded! Well not so, but everything does have a finite lifespan, so look at the curtains closely to see if they are worn or sunbleached or motheaten before you start the project.)
There are two or three different styles of plastic hooks depending on they year your Airstream was manufactured. Airstream sells them, Camping World carries 2 of the 3 common ones, and I'm sure Inland Andy has them too. They might be available from Hirsch - a manufacturer of common drapery hardware or a custom drapery shop might order them for you.
I just said fergit it and picked up a s-load of them from the factory - $38 per hundred if I remember.