The peep sight would not be a problem. Thompson Center sells a tang style peep that would fit that rifle. Because it is a .45 caliber and the model of the rifle unknown, I would not recommend a Green Mountain Barrel for it, simply because I am not sure it would even fit.. Instead I would suggest that you get a used .54 caliber Renegade. They have a 1" on the flat. Then you can get a Green Mountain Smoothbore rifle in .62 caliber and use that. Its a 20 ga.

Also welcome to the forum. Why not post a picture of the rifle if you are able. Hawkins, Renegades, and Seneca's have some definite characteristics. Perhaps we could help identity the model of it.