Thanks for the advice guys. Much appreciated. Do you think I would have to clamp it?
You wouldn't be able to clamp it unless you open it up first with a knife/flathead screwdriver,
For a crack so small it isn't necessary in my opinion. Soak the area in pva (watered down if necessary) and leave the bat in a position where gravity will pull the glue into the crack overnight,
Sand off the residue left around the crack you're good to go.
As advised above, there is the potential for this to be a very small and insignificant crack, it's hard to tell from pictures, so I would try and see if you can sand it out first.