I would say yes, Kas'im beats Dooku in sabers. Being called "The greatest swordsman of his era, perhaps of any era." is not something that should be taken lightly. Kas'im also bested Bane in saber combat - Bane only one the Force part of their duel, and that could arguably have been luck, but that's another debate. He completely obliterated a Rancor. Also, I don't have the exact quote with me, but he mastered every form of lightsaber combat to the highest degree and practiced all the forms for hours a day (or something like that).
He was a match for Bane, who was stronger than the entire rest of the Brotherhood of Darkness combined (stated on the PoD cover-flap, I believe).
Dooku is good and would likely put up a good fight against Kas'im, but I can't see him winning. Nor overall, anything Dooku throws at Kas'im I think he could block. After-all, a Force Shield, thrown up at the last second, was enough to block the portion of Bane's attack that was directed as Kas'im, and that was an attack large enough that it took Bane a few seconds to conjure it, and it was powerful enough that had it made contact with Kas'im, it would have turned him into a pulpy liquid. What does Dooku have that can top that?