Traditionally, there have been three routes to get into hand surgery: orthopedics, plastics, and g-surg. The first two count for most of the cases. So, you may be able to score a hand fellowship after g-surg.
As for adult reconstruction, I have never heard of anyone doing one without doing an orthopedic residency first. When you would go in practice, you would need to be board certified in orthopedics since there is no subspecialty certification in adult reconstruction and that requires having completed an accredited orthopedic residency.