You should within mind that mind that softball bats are lighter and while playing baseball it will most likely get dinged.
I catch with my left and throw with my right, so i am on the lookout for a form-fitting Baseball Glove for my left-hand. The kid must comfy enough to carry the bat. https://Www.storeboard.com/blogs/sports-and-fitness/step-up-your-game-with-these-must-have-baseball-batting-gloves/5950606