Spent a bit of time this arvo having a bit of a measure-up.
The rear wheel needs two differently sized steel discs to mount it up on. One on the inside and one on the outside. The two discs need to be 130mm & 123mm.
The front wheel does not need a disc / hub as it can be mounted directly to a spindle, however the standard bearings will need to be replaced with bearings that have a larger ID as the standard ones are only 10mm.
The dimensions of most go-kart stub axles appear to be 5/8" which equates to 15mm for the imperially challenged. (Big thanks to Ken for the previous links).
So after a bit of googling I found that a standard 6202 bearing is 35mm OD and 15mm ID which is about perfect. It is ever so slightly larger on the OD than the original bearing (34.5mm) but I can machine the hubs to suit. There are some 34.5mm taper bearings available, but they are pretty expensive so machining the hub seems to be the best option to me at this time.
The rear hubs will also need to be machined to get a flange to fit inside as the bearing housing protrudes past the rest of the hub. I checked on my lathe and with the tyre removed from the rim and the gap bed removed from the lathe I think I can just squeeze it in without having to disassemble the wheel.