I do not use a velvet helmet cover for my skull cap. In my area, I see a TON of Eventers use the black silk that came with their helmet for the dressage phase. I am one of them. Charles Owen J3 Skull Cap Helmet and Equestrian Skull Caps | EQUESTRIAN COLLECTIONS.COM
If you want a "suitable" helmet for the dressage phase, why not just keep your current show helmet for that and the stadium phase and save your skull for the xc phase?
I wear my Skull Cap for all 3 phases, same black cover for all 3.