Vall,
I certainly can't argue with you about your own rifle, I have never even seen it, much less made a chamber cast. I noted a couple of these rifles on Simpson Ltd., but someone beat me to them, maybe you were one of them. The fact that you can use 38-55 cases means the cartridge is based on the British 360 case rather than the German Mauser Base case. Dixon (European Sporting Cartridges) lists a 9.5x47R with the Mauser Base cases, but not one under those based on the 360 based cases. There is, however, a 9.3x45R and also a 9.3x48R listed under 360 based cases, but only in the German form (German form chambers will not accept English form cases without resizing, even if the same nominal length). Indeed, 9.3 mm is smaller than 9.5mm, but old rifles were often found to use bullets with a smaller diameter than the groove diameter, depending on the black powder to obturate it to fit. The grooves were deeper, to (hopefully) provide room for black powder residue. Modern practice is to use a bullet the same diameter as the groove diameter. Also, old rifles often had chambers a little longer than the case length (maybe to provide room for residue?), and some had a neck and lead the same diameter, making the nominal case length hard to determine. I think your rifle could be chambered for 9.3x45R, 9.3x48R, or 9.3x57R, based on the variations discussed above, especially case form. Since I don't have a Husqvarna and HalfaDouble does, I suggest you PM him to solve the question. If you haven't made a chamber cast, it will be necessary to do so.
Mike