Welcome to GBO! Although I don't have a Shikari, from all that's been posted here, they are great rifles and have excellent ballard cut rifling, the frame is not of the same strength as current production rifles, so you would be limited to trapdoor .45-70 levels, H&R won't fit a barrel to any frame made before 1987, I don't know if the current barrels will even fit that frame, someone with one of em will have to answer that question for ya. If they do, it would have to be a low pressure caliber, seems to me they were originally offered in Muzzleloader, 44mag, 22 Hornet, .357Mag, and of course shotgun gun combos, but don't quote me on that.
Hope this helps a little,
Tim