Start here: hand reconstruction is usually funded, together with the therapy that matters most
Before any conversation about private cost, it is worth confirming what your own health system already provides, since hand reconstruction, as treatment of injury, infection or a congenital condition rather than elective cosmetic surgery, is usually funded in developed health systems.
What matters particularly here is that funded pathways generally bundle the surgery together with the hand therapy that follows it, delivered by the same service as a matter of course. This combination is the main advantage a funded pathway has over private treatment, since an operation without the therapy that follows it is half a treatment, and therapy is the half that actually decides how the hand works afterwards.