Ok, this isn't about wiping out something that you can fit your hand into--that's easy. This is about when you get something (cerium, moisture, dust, dirt) on the inside of a piece with a very small opening. Since my Spheres and Resistenza both have very small openings, I've figured out a range of ways to effectively wash and dry work you can't get your hand into.
This problem is thornier than you'd ever guess. If you just fill the piece with water, rinse and drain, you'll end up with a sense of satisfaction you'll realize is false--usually the next day when you notice that there's a ton of condensation coating the interior of the glass, that resists all attempts at drying. If you can get it dry, you'll often end up with water spots; a situation likely way worse than the problem you were trying to fix in the first place.
Here's what I do to wash interiors of sculpture and vessels. Note that if it's a small localized stain, I might first thread a wire in that's had the end tightly wrapped around a tiny piece of alcohol saturated paper towel and rub the stain. If that doesn't apply try this:
1. Fill with water and shake
if that doesn't work
2. Water w/dish soap and rice (only if it easily fits through the opening or you'll not be able to get it out) and shake
if that doesn't work
3. Water w/dish soap and a bunch of small lead shot and roll around (don't shake)
One of these has always worked. Others have also had success with Polident instead of soap.
Rinsing is just as important. For any work that is wet on the interior I do the following:
4. Fill and rinse with water until you get all the soapiness out. I put water in, shake, then turn upside down and shoot a half-second of compressed air in which forces the water out. A few shots of compressed air and the water is all displaced. I generally rinse a few times like this until there's no soap.
5. Then rinse 2-3 times with alcohol, but the 99% stuff--not the 70% from the drugstore since it has too much water (the 30%) in it. If you've got a super tiny opening or something that's tough to dry, acetone is excellent since it evaporates so well.
6. Set the vessel upside down to drain for a couple minutes, then thread a very thin air line that's connected to an aquarium pump into the opening. This will create positive pressure and force out any liquid; left overnight it will evaporate any alcohol or acetone. I set the piece on a cardboard ring (left over from used up packing tape) that has a hole in the side which I run the air hose through. This way the piece is supported upside down and the airline isn't crimped. The next morning it should be clean and bone dry.