Being Thai, I'm pretty sure that the resemblance is merely coincidental. The words for "fish", and "swim" in Thai are:
fish: ปลา
[pla:]
swim: ว่าย[wa:i]
Thai has a word for "fish" that was borrowed from Pali/Sanskrit:
มัจฉา:
[mad-cha:]
which sounds not very close to the mentioned Slavic word.
I'm more curious in how words like "elephant", "avatar", "immortal", which Thai borrowed from Pali/Sanskrit as เอราวัณ [e:-ra:-wa:n] อวตาร [a-wa-tan] อมตะ [a-ma-ta], sound like in Slovic. (NOTE: The more common word for elephants, which is not a borrowed word, in Thai is ช้าง [cha:ng].)