Most likely not. While the trend toward smaller grips on tour does have some truth to it, not everyone is following along. In my time stringing for some of the best players in the world, I haven’t noticed many using an “extreme” small grip. 4 3/8 is the most common size on tour, in my experience, just like it’s the most popular one amongst club players. The main difference is that they have most likely done exhaustive testing to make sure it works for them (I believe Venus and Serena use 4 5/8!).
You could experiment to see if a handle size change would help you, but only under the supervision of a qualified technician. Just like a worn grip, one that’s too small out of the box can lead to injuries.