I’m not sure I understand the connection of the clarinet being more Yiddish sounding and you wanting the play the sax, but I will say that the sax is a much heavier instrument, so it would depend on your physical makeup. If you are bigger and stronger, then you could play the sax, but if you are smaller and not as strong, then I would go for the clarinet.
But still, if you’re a frum girl, why wouldn’t you want to go with a more “feminine” instrument, just to buck the system?
BTW, the viola is a string instrument just a bit bigger than the violin.