The danger is hitting your approach past the hole. Make this mistake and you’ll face one of the most challenging putts you can imagine. From the back-left to a front-right pin it’s a roller-coaster ride. Expect a lot of three-putts.
Although the saw grip falls into the “alternative” or “unconventional” category it may be the most natural hold of all because with the saw grip your right hand never strays from the correct impact position from start to finish.
In both cases the key is to adjust your shoulders so that they sit parallel to the slope you’re standing on while maintaining good balance so you can swing through the shot. A good practice swing is essential so you can “see” where your swing is bottoming out and making a divot. Use the divot’s location to confirm that you’ve positioned the little white ball in the right spot (i.e. before your wedge strikes the big green one).