While wooden shafts occasionally 'can' be shortened, it is important that they be shortened from the 'rear'. Your cart has drop heel shafts, and it doesn't seem feasible to me, from the picture, to try that. You MIGHT be able to order a shorter drop heel shaft, but that would entail dismantling the cart--and, you would STILL need to make the shafts closer together where the tug loops hang.
Wheels are mighty expensive, and would also need finishing. You'd need to be sure they would 'match' the cart's axle set-up and hubs.
I wouldn't try to 'cut down' this pretty cart, if I were you. The MOST important feature of a two wheeled cart is proper BALANCE, and THAT could well be thrown completely off by 'messing about' with what would amount to extreme' changes.
Does the cart have a seat that adjusts forward and back? If it doesn't, it would be even MORE likely that you could mess up the balance by messing around with trying to 'shrink' it for a notably smaller animal than it was designed for.
In a two-wheeled vehicle(cart), there should be VERY little 'downward pressure', i.e., weight, on the shafts where they pass through the tug loops, when the 'load'is IN the cart(load meaning driver!)--you should be able to stand between the shafts and 'hold them up' with one finger. The shafts should 'put significant weight on' the tug loops ONLY when the cart is empty, and when the driver/any passenger gets in or out; otherwise, when the 'load' is properly seated, the shafts should 'float' in the tug loops.
You can SEE this happening, and it happens best with an open tug and holddown straps, not wrap straps. You can also see it NOT happening,and the weight 'dropping onto' the tug loops(and therefore, fully onto the (usually narrow) harness saddle, and therefore, your horse's BACK!) when you forget and LEAN FORWARD while seated in the cart...the balance is as easily 'disrupted' as that!
This fact BEHOOVES drivers to always be aware of how their position in a cart can disrupt proper balance, and result in DISCOMFORT for their horse(as the nearly ENTIRE weight of cart AND driver/passenger is NOT going to be pleasant when transmitted to a 2"or so wide area of the horse's back-and that's what happens when balance is 'off'!) Many newer drivers have NO idea of this phenomenon, but should learn about it, for their horses' benefit. Sit up straight and all the way back (reasonably) in the seat--not necessarily 'leaning back', just sitting up straight.
This can happen in ANY kind of cart...from Frontier EE to 'name' brand show ring cart--I have SEEN it in both. I had a student several years ago, a substantially-sized man. I had to CONSTANTLY remind him to 'sit up', straight back, and all the way 'into' the seat, of a show cart-or he was putting an uncomfortable pressure on his mare's back...
My advice would actually be to take the cart to a KNOWLEDGEABLE cart builder for a professional evaluation of whether it would be 'successful', from the horse's point of view, to make the changes you propose--or, as others have suggested, just look for a larger driving pony--one the size the cart was built to fit!
[i cannot IMAGINE 'cutting down' a cart that was for a 13-14+ hand draft pony to PROPERLY fit a miniature, even a big B....it might 'look' OK, but I'd surely be concerned about the genuine comfort of the miniature being asked to pull it...how it LOOKS after alterations is not what's really important....]