I wouldn't convert that rifle. You'd lose value and history by doing so.
I have an unbroken set of American Rifleman magazines, from 1929 to last month's issue (900-plus mags!).
In the 1950s and 1960s, particularly, many fine, old Scheutzen rifles -- brought back from Germany by G.I.s -- were converted to more popular calibers.
The result was that a lot of rifles were butchered by "garage gunsmiths" who ran chambering reamers in with an electric hand drill, and other horrors. Makes a fella want to cry!
I'm still flabbergasted at the reader who, in the early 1950s, wrote in to ask if his Winchester 1873 rifle could be converted to .222 Remington!
I looked through my personal directory to my American Rifleman magazines and could find nothing on the 8.15X46R.
I don't find such a cartridge listed in Cartridges of the World, 8th edition, but I do find an 8X46R Sauer that seems to fit your description of looking like an overgrown .22 Hornet.
Is this the same cartridge?