Given the recent photograph you shared, I retract my recommendation to use a hospital plate. The resected area is significant and a hospital plate would not add value.
Booting over that shoe is possible but could prove a challenge and I don't think there will be a lot of benefit.
Paint the resected area daily with an astringent (iodine, betadine, etc) to toughen exposed tissues against moisture, clean as needed and wait for growth.
As new growth comes down, your farrier will want to manage any distortion in the hoof capsule over the damaged area. The new wall tends to bulge over these areas.
Next time the farrier resets, suggest well placed clips to further stabilize the existing hoof capsule.
I'd also shoe the other foot to improve balance.