Leather can be thinned down in a process called splitting, and is done on.....a splitter. Splitters are typically very expensive, so I think cost would be prohibitive. Another method is called skiving, in which a razor blade (usually mounted in a tool that holds the blade at a slight curve) is used to slice leather off of the flesh (rough) side. Leather thickness is measured in ounces, which equate to 64ths of an inch...8 oz = 8/64ths=1/8th inch. Most of my wallet/bill fold work is done on a maximum thickness of 4 oz. When the leather is thicker than that, you can experience some difficulty in bending the wallet.
Your statement indicates that the leather is pretty thick, so the easiest option is to check around for a leather supplier near you. If there isn't a leather supplier, you might look for a Hobby Lobby, as they sell small craft kits (including a simple wallet). If that yields no results, you may need to order a kit online. For beginner kits, Tandy Leather Factory has something right up your alley...and budget. You can find them at this address.
There are also suppliers listed at the top of the forum page which may have something you're looking for.
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