You only need to worry about the soft tissue issue if you are doing the fat gripz with curls. I don’t know how common this is, but I had the problem when using a fat bar for it.
Fat gripz should help with increasing grip strength, but you should probably look into other strategies as well. There’s a lot of good stuff at Ironmind In particular, I have seen Louie Simmons recommend this for increasing hand strength for deadlifts. Expensive, but you might find a cheaper version somewhere.
Be sure to use plenty of chalk. In the meantime, if your grip is lagging, use straps on your heaviest deadlifts.