I have some hide that is a little thick for wraps (.035") any way of making it thinner??
One method not mentioned is to press it by running it through a pair of fabricated rollers similar to the ringers on the old fashioned washing machines. It is too thin to split or skive any further. I'm no longer in the business but in the 70's I made hundreds of belts and holsters, specializing in floral carving, and I would "wet and press" leather that was too thin to skive (or split).
Cut the wrap groove deeper to match the leather (and hope they never want to go back to linen because filling that wrap groove with epoxy and recutting it is a pain,) OR sand the wrap itself.
Pls don't do that.
Lord, 035" a side ?
That is only .010" per side.
To answer the original question you can feather the ends to .025" with a sanding block in just a few minutes. If it was me I would cut the groove deeper for the nicest job and just build it back up later if you go back to linen.
Why?
Quality leather isn't that expensive.