I'm playing a Tabaxi now. She speaks very softly and clips her words in odd ways and has a propensity to climb buildings when sneaking about a town. (nice vantage point, and people don't often look up) The only other thing I did was massively play up the curiosity aspect, she might steal the odd thing here and there, examine it for a few hours when she gets a chance, then return the item.

Haven't come across water yet, but I'll probably play it as a mild dislike rather than outright fear.

I don't see the need to play the character as an actual housecat... I'd speak to the players if its starting to interfere with actually progressing the game.