I removed my pump and let it drain for a while, then stuck a 2x4 under the front wheel to get it so it wouldn't keep dripping for days. Then I wiped up all the oil in the exposed passages and ports and wiped down with brake cleaner, RTV-ed, and installed the "new" pump.
I don't think you could keep oil from dripping though unless you had the engine standing on its end though in that case it would probably start dripping out somewhere else. At any rate it'll only need a couple glugs to top back off.