A No.2 Joseph Dixon-style edge beveller would be my choice, but that's because I have one. Failing that, 80 and 120 grit Aluminium oxide paper which is fresh and sharp can be used to advantage.
To tidy up any straggling fibres the traditional method is gum tragacanth and a bone folder, and use friction to heat and seal the edges. A piece of hardwood can be used if you don't have bone. If you don't have the gum, you just need an appropriate mucopolysaccharide so spit works too.
I use a combination of these, plus Fiebing's Edge Kote to finish the edges of my leather bags. Wax (proofide) over everything when you're done to keep the water out.
ETA: If you want to actually skive the edges thinner, beyond the normal edge bevelling, then given the awkward clearances of a saddle I'd probably use a scalpel rather than a skiving knife. Swann Morton No. 3 with a No.11 blade has a small triangular blade which might work.