Clubs are designed to stay in balance during the swing. You should not need to grab on to a club -- choke a chicken. Squeezing the club causes tension in your forearms (and elsewhere) and that creates lots of problems including a loss of freedom in the hands which kills distance.
If the club turns before you get to the ball, something is wrong with the position of the clubhead during the swing. Again, the clubs are designed to remain on balance throughout the swing. You should be able to hold the club with just a few fingers in each hand. My "drill" is to use the thumbs and the pinky and ring finger on my lead hand and the trigger finger on my trail hand. I let all others try and stay off the club.
If the club turns when you hit the ball, you are missing the sweet spot badly enough to have it try and turn. Often on the toe. Solution here is not to squeeze harder.
That said, newer grips will allow you to hold the club lightly and not have it slip or feel like it could slip.