At the risk of being completely wrong, I suspect that is loose wood fibres standing up in response to the moisture in the stain. However, I cannot give any advice on the right sandpaper grade to use for very gently removing them, as I have no experience sanding stained timber.

With my build I lightly wiped down the body with a damp rag, waited for it to dry, and then lightly sanded at 5 degrees off the grain to knock off the loose fibres. But this was prior to applying any finish.