Well my name is also spelled Kasia and I'm not Polish nor have knowledge of the Slavic language but I pronounce my name as Asia with a "K"... sorry if that's strange or rains on anyone's parade.
My Polish great-grandmother is named Catherine, but called Kasia within the family. She pronounces the name KAH-sha, but the "sh" sounds different than the typical English "sh". Its pronunciation falls somewhere between "sh" and "j", similar to the "j" in Jacques.
Kasia is pronounced KAH-sha. [noted -ed] As a child all my dolls were named Kasia. Oddly it was the name that most children in Poland chose for their dolls. I suspect because the sound of 'Kasia' has an incredibly sweet and snuggly feel to it.