Your grip in OL will improve naturally over time. There are not a lot of ways to train the hook grip to be stronger except to just use it. If you do want to do something helpful, any kind of static hold will be most effective for what you want. Hanging from a chin bar is a good one, as are any other holds with a heavy bar for 20-30 seconds.
Most weightlifters dont train the grip directly, in fact their hands take such a beating that they usually use straps on some of the snatch workouts just to rest the hands.
If you think your snatch would be that much better with straps... try one workout with them. I think youll find that they wont help as much as you think, but I could be wrong.
Its not unusual for a competitive lifter to snatch a bit more with straps... maybe 5kg. What I find often happens, is that as you are going up, you will make each new PR with straps the first time, then within a week or two, you will make it without... like the security of straps helps you break barriers, but once youve made the weight and gotten it overhead, you soon find that you can do it without the straps.