I've used both Kangaroo and Hairsheep (a cross breed of a domestic sheep I'm told) leather for leather covered pads.
I've always acquired it from Columbia Organ Leathers in PA.
They supply the stuff mainly for the restoration of the musical instrument(s).
They can supply it in various thickness all the way down to .008/.010 with some of the same offerings up to .025.
Other types go thicker and up into the .035 to .050 range.
Some are white color, but there are also brown, black and maroon.
The Kangaroo leather is quite something to work with. Sometimes you don't even need to soak the leather in water to get it to stretch over the pad and get the wrinkles out.
Some States ban the import to their State of Kangaroo leather in any form,,rough leather or in the form of completed clothing or foot wear.
So don't be surprised if that becomes an issue.