Well, having good grip strength isn't going to hurt. You'll also rarely find someone who is strong with a weak grip.
But, if you're just doing it for fun and don't really care, sure, straps are fine.
I'd say your best bet for the moment would be to use straps for DL, and all other pulling without. If you can, add in some specific grip work - farmers carries, suitcase holds, hanging from a bar for time, etc.