Small Bespoke Hand Shoulder Plane 5/8" Diameter
The wedge and iron seems to be fairly firmly in there and I haven't tried to take it out. It's probably a fairly simple job but it wasn't terribly interested because I didn't want to destroy the wood. The total diameter across the shoe is 5/8 of an inch and the total length of the shoe is an 8 over 5 inches.
This plane looks to be home made.