If you require 2mm driving axles Ultrascale will often supply that size axle if you order a set of wheels. Suggest you give them a call to ask if they can help. It’s usually a matter of making a new plug for the axle in the mould but I think they would only want to do that if they have a firm order. It might also be possible – again you’ll have to ask specially – for the wheel to be moulded with a larger boss on the back, which might remove the need for packing washers and also provide a longer axle hole and therefore grip and stability – it’s a very big wheel and a very small axle.
The other wheels: Just a matter of opening out the holes in the front bogie and the tender, or widening the slots in the tender chassis if it the usual Hornby method, although on the tender I would think pulling the wheels out in the axles would be OK. The rear truck on the engine: I would just run it with the flangeless Hornby wheels as supplied, maybe just relieve the bearing a touch so the wheel slightly touches the track. The extra width of a Hornby wheel should nit be obvious and will help as the engine goes around curves.