According to Dunlap the .25-20 SS uses an 8" twist, which, I would think, would stabilize any .25 caliber bullet known to man. Such a rifle could easily be converted to .25-30 Winchester (6.5X52R), which is capable of sending a 7.6 gram projectile on its way at 650 meters per second (117 grains at 2112 feet per second). Assuming the barrel steel is of such a nature that it can stand up under increased pressures and velocity, it could be a useful little weapon.

A more potent solution would be to rechamber to .250-3000(R) or .257 Roberts(R), using 6.5X57R brass to form the cases. I have had for over 50 years a Winchester High Wall in .250 Savage (R), which has worked without a flaw for me.

Then there is the possibility of the .25 Ackley Improved Krag, which brings with the capability of performance approaching that of the .25-'06. I have had a Sharps-Borschardt rifle in that caliber almost as long as the .250-3000R.

Probably the best solution would be a rebore and rechamber the barrel to 6.5X57R or 7X57R. Either one would turn this vintage single shot into a useful hunting rifle.