Vegard, caution: There are two entirely different cartridges named 9.3x53R, none of them German and not interchangeable:
The 9.3x53 R Finnish. This is the cartridge Sville is referring to. Though occasionally still available from SAKO, it is rarely encountered outside Finland.
As you live in Switzerland, the combination gun you found is more likely chambered for the 9.3x53 M26 Swiss load. Several combination guns and single-shot rifles were made in Germany for the Swiss market. I own an o/U by Schmidt & Habermann, Suhl. I got a die set from CH almost immediately. Cases are a problem here: I make mine from S&B 7.62x54R Russian cases, but 9.3x53R Finn cases may be even better. For use in my chamber, I have to thin the rim slightly. Then the cases have to be fireformed to be blown out to the "improved"shape of the Swiss number. These make usable "Swiss" cases, though 0.15mm small at the base.
You may find some info on both cartridges in these threads:

http://forums.nitroexpress.com/showflat.php?Cat=0&Number=150441&page=0&fpart=1&vc=1

http://forums.nitroexpress.com/showflat.php?Cat=0&Number=171575&an=0&page=3#Post171575