Leather is a surprisingly comfortable material in just about any application. It also has the ability/feature to change colour and feel with use and time, probably almost always for the better. I would try it and see how it works.
I imagine the straightness of the cut and the quality of the wrap (your skill and ability to get it on even and tight) are as important as the material. A periodic application of a waterproofing or maybe a wax might be beneficial to avoid damage from sweaty hands and snot and spilt Gatorade.