In a 1920 issue of American Hatter, something called the vel-comb is advertised for hats with nap. I'm having trouble linking it here, but if you google search vel-comb american hatter, its the first one that comes up.
Iyor, thank you for the keywords. I found four ads searching for Vel-Comb, but no drawing of this tool.
From the last ad (which you might have trouble reading):
"Robert Swisky, assistant to Mr Davis, has invented and patented a brush for velour hats called the Vel-Comb. It is a comb of wire with a velvet handle, and restores the surface of a worn velour to its original condition."
A wire comb, then. That could mean a lot of constructions, though...
Any ideas?