Even easier (and easily un-done if you change your mind) would be to wrap an overgrip flat without overlapping on the bare racquet handle, then put the leather over the top. It'll be the same size as leather plus overgrip, but in reverse, giving you the surface feel you like.
My tip to anyone putting a grip on their racket, don't staple, get some double-sided tape, remove the beginning section of the tape on the grip and replace with a small trimmed section of your new double-sided tape. It sticks and starts the grip wrapping so much better.
"Tennis is just chess with balls....zugzwang"
"The older I get....the better I was"