I would vote more for the Sharps, although both are possibilities. MY reasoning or thinking is a .45-70 shoots government ammo which is in easy supply and access.
However, one can counter that by looking at Custer and his Remington where its ammo is a private purchase/private ordered deal but yet he had cartridges. I guess since officers do not intend to shoot much, a box or three of shells could stretch a long way.
I used either a M1875 Officers' trapdoors, or for a little.. a Gemmer "trapdoor Hawken" in .45-70.
I do not have it handy, or remember where I put it..
but I had an article on some of the 7th Cavalry officers including Custer going on the "cheap" and buying "obsolete" M1868 or M1870 .50-70's on post for a long arm at.. IIRCC.. $12 or $14.
And for my Apache Wars stuff, I used a Remington M1875 in .45 Long Colt instead of the Colt or Schofield.
Officers had to buy their own uniforms and kit, as well as arms.. so much is possible. Plus they were also given a break and were allowed to buy and wear enlisted stuff for their own use.