I never heard of hardwood dowels causing splitting of a buttstock when used to plug screw holes in this manner. You shouldn't have anything to worry about.

I have seen stocks that split when lead shot is stuffed into a hole in the butt in order to add weight. Over time, the lead shot oxidizes and swells, eventually splitting the wood.

Voting for anti-gun Democrats is dumber than giving treats to a dog that shits on a Persian Rug