Whether you're just touching up an old stock or completely refinishing, you'll find that, even after a good degreasing, the sandpaper will clog up fast. For just touching up, no big deal, you're not doing that much. For complete refinishing, it is a big deal, you'll go through a lot of it. So if you're taking all the old finish and surface off, I will suggest using a scraper.
A scraper will cut fast and clean, and won't clog; at most you'll just have to wipe off the edge every so often. You can buy commercially-made scrapers at woodworking shops and suppliers, or you can make your own. Two ways to make them.
DISCLAIMER: the first method yields a good scraper that will, if you're not careful, slice you worse than what you're working on. Use gloves and be damn careful, and if you start hemmoraging don't blame me.
The simplest, cheapest way is to use glass. Get something like a mayonnaise jar, wrap it in something and break it, or break a piece of almost any piece of glass. The edges will be VERY sharp, and if you're not careful will slice you as you work, so use gloves and BE CAREFUL.
The other way is to make it of metal. What was recommended to me some years ago was an old hand-saw blade. Use a Dremel and cutoff wheel, or a grinder with said wheel, or just use the corner of a grinding wheel to cut a groove along which you can break a piece off. Then grind the edges you cut square, and as smooth as possible. Here a sanding drum or belt sander works very well. You also want to touch up wth sides, to the edge is square a smooth. Now comes the tricky part. For a very fine cut you can use it as is, but to take off material fairly quickly you need to forma 'hook' along the edge. The way I was shown was to clamp the piece in a vise, take a screwdriver with a round shank- the smooth part of a round file, basically anything rounded, smooth and hard enough will work- and push and pull it along the edge, tilted toward the edge you're forming the hook on. It forces the corner to curl over a bit, giving you a very aggressive cutting edge. You can do all sides if you wish, I'd suggest only hooking the edge or edges you plan on using, so you don't have to worry about cutting yourself on a fresh edge.
Generally, with glass or steel, you want a piece with a curve to the edge, which will let you work around the curves in the stock better. Hold the scraper(Carefully, I said!) with the working edge trailing your hand; you're not pushing it into the wood, you're dragging it across the surface. A little trial and error will show you the best angle, that varies according to the wood and the tool. Drag it a ways, see how deep and wide it cut, make the next pass and observe; you'll find the best angle to work the piece at. You'll also produce lots of fine shavings, and in the case of an old gunstock you'll be removing the crud at the surface along with the wood. You can work the entire piece, or just in an area that needs serious cutdown.
When you're done, you'll have a stock with a much cleaner, smoother surface, ready for sanding. And you'll have much less trouble with the sandpaper clogging.
Note: I'm going to splice this into the 'Cleaning' post, so as to keep it all together.