As to the washing, the main reasons for not washing leather are that 1) it dries it out and 2) it may leave watermarks.
Some of the newer leathers are actually washable.
If you're using scraps, I'd be tempted to stitch a scrap to a plain contrasting fabric, mark the size, run it through the washer to see what it does (shrink, bleed, dry out, leave watermarks on the leather, etc). I would not expect shrinkage or distortion but it may bleed...or not. Drying could be countered by using a very mild soap instead of detergent. Watermarks? You may actually like the effect. I'd give it a shot.