The Uberti 1873 replicas are not intended for use with hot ammo. It might not harm them to shoot just a few rounds, but the design is simply not up to it.
The original design started with the Henry rifles of the early 1860's and goes as far back as the Volcanic rifles and pistols of the 1850's.
The Uberti 1873 rifles are magnificent very close replicas of the original Winchester rifles with the only real divergence being the striker assembly and the use of a coil spring and ball bearing to power the sliding receiver cover.
None of this can be seen from outside the rifle.
The new Japanese made Winchester 1873 has a striker assembly that's quite different and may have other differences from the original or the Uberti versions.
If you want an authentic Winchester type lever rifle you can shoot hotter ammo in, buy an 1892 type rifle. These are offered by several companies including the South American Rossi, one Italian company, and I think Winchester offers a Japanese made version.