Rossco, are the hubs that you have bolt on hubs, meaning they fit direct onto the studs on the outside or the brake drum ? If so, the change to wires is no more difficult than changing 4 wheels. Any pics and we can tell you what you have .... Wires will need rubber liners to cover the spoke nipples on the inside tubes and yes it can be hard to find someone to fit tubes and tires and then balance "old school" for wire wheels.
If they are not bolt on hubs, it gets more complicated fast, as you need to change the following:
You need "disc brake" front stub axles and kingpins - same for wires or standard wheels
Possibly A frames if worn as mentioned above, and definitely new fulcrum pins and cotter pins.
The used front hubs you have will likely need new bearings and that is the safe way to go.
You also need the disc brakes and calipers, and a new 3/4 " Master Cylinder required for discs.
Then at the rear, if you have the hubs with axles of a late model car, then as these are shorter than Bugeye axles, you could press the axle shaft out some to better engage at the diff and at the hub as mentioned above. If they are off a Mk2, then they should be the same length as a bugeye axle, but these are rare.
You also need the 3/4" wheel cylinders, which are available from a Morris Minor, as these are the correct orientation for the Bugeye backing plates and handbrake rods.
All up, doable in a weekend... or two !
Cheers
Lew