Un-buffered mats are always the safe choice when framing organic things that may be alkaline-sensitive.
I don't think we don't know enough to give concrete advice on mounting for this job, but hinging may not be my first choice. Starch paste would be the safest adhesive, but it may not stick to leather that has oil content.
How thick is the leather? Does it have texture? What kind of paint and/or other media have been applied to the skin? Does it have an irregular shape, or is it neatly cut? Are thre edges to show, or be covered by the window mat? Is it flat, or wavy/cockled?
For a typical leather of up to, say, 16 x 20, I would consider using a fine mesh fabric overlay mount. That is, prepare a mount board covered with a few layers of polyfill and a fabric background. Lay the artwork on it and then wrap it in Stabilitex or Crepeline. The polyfill provides a slight tension to make the assembly slightly rounded, helping to hold it in place.