As far as I know, the cases are same as modern 7.5 Swiss, only loaded with black powder. I also believe that one could get by using reduced loads of smokeless powder (such as 4895), as the steel in the Schmidts was of decent quality. I definitely think anyone is well advised NOT to use modern Swiss ammo, however.
A parallel example is the original 1888 British Lee-Metford rifle; Originally chambered for a black powder .303 round, it made the transition to Cordite successfully as far as handling the pressure was concerned. It was the Metford rifling being quickly eroded by Cordite that prompted the switch to Enfield type rifling. The rebarreled guns served well into the 20th century with no real problems handing smokeless powder.
Metford and long Lee-Enfield shooters today generally handload their ammo to Mark VI levels, originally intended for the long Lees such as the early Mk Is and IIs, and the first SMLE, the No. 1, Mk I.
Some decades back, I occasionally shot my Lee-Metford with reduced 4895 powder loads and had no problems other than lousy accuracy due the completely trashed Metford rifling.
Given that the general quality of the 1889 Schmidt-Rubins and British Lees are comparable, I wouldn't see any problem with loading reduced smokeless powder loads for it.
As always, YMMV.