You can actually repack a hub without removing the freewheel. Loosen the locknut from the cone on the NDS, remove both from axle. Pull axle. Commence to cleaning cones and races.
Even with small fingers it's a little difficult to fully clean the race on the freewheel side but it can be done. Flush the bearing race with WD-40, since you have some on hand, wrap a square of old T-shirt over your pinky and wipe around in there, repeat as needed.
If you don't mind taking the time to pick up a freewheel remover that makes it easier, however.
WD-40 on wood, eh? Very interesting.