How do I safely get glue off of wood that's to be stained?
Mineral spirits should work.  If not, I would use Goof Off (or similiar).  There's lots of glue solvents, and wood glue should be pretty easy for any of them to handle.  I think it would dissolve right off, but I'd probably test it on any scrap red oak you have just to make sure it doesn't discolor.



Cotton may work, but I wouldn't be afraid to use a fine steel wool here, probably 000 like you would use for finishing polyurethane.