BS”D
Antistatic spray and then a brushing with a hat brush should do it. I’m with Jothar though and I keep my velvet yarmulkes for Shabbos. When this crop becomes unusable I am switching to cloth for Shabbos as well. Cloth was good enough for my Rebbe ZYA and it is more than good enough for me.
Regular cloth yarmulkes are hand washable (soakable).