Why not カザクスタン ? The Cyrillic word does have a k (but I am not sure whether is is actually pronounced).
At least in the last few decades, when Japanese people katakanize foreign words, they do so based on the sound of the original language, not on how it was adopted in English. For example, Eiffel Tower is エッフェル塔, not アイフェル塔, because its French pronunciation is closer to エッフェル. Johann Sebastian Bach is バッハ, not バック nor バッカ, because its German pronunciation is like バッハ. I know nothing about Russian, but according to the Russian pronunciation of Kazakhstan , I think カザフスタン is reasonable.