I have always used just a tack rag, to remove the dust, and usually apply stain with an old sock, or some sort of terrycloth.
I'm not too sure i would wipe the wood with any type of liquid before I stained it, since stain is absorbed into the wood. If any parts are still damp, you will have a blotchy finished stain job.
I dont think you need to wipe it with anything more than a tack rag.
If you are set on a wet wipe, I'd use naptha.
EDIT:
Removing duct particles isnt critical at the staining process. Since stain is absorbed into the wood, you wont seal any particles to the surface.
Be especially careful when you begin to polyurethane the project as this is when you will seal foriegn material to the finished surface.
Pick up some fine steel wool, and a few tack rags...