Don't go into mourning over the loss of a pre-war Type C stock, because that isn't one. It is (or was) a pistol grip "combination stock" which will take both the M1903 and the M1903A3 barrelled actions. Most of those were made as replacement stocks, and they are almost always thicker and "clubbier" than the pre-war real C stock. There is plenty of wood in those wartime stocks for a cheekpiece; it might be a bit tighter fit with the slimmer C stock.
Jim
Jim