I'm really glad mine is the 9.5 instead of the 9.3. I use my .38-55 dies to load it, and run .38-55 bullets through my Lyman sizer to make them .376" diameter. I trim the .38-55 brass 1/10" approx.

My measurements showed the 9.3 to only be .006" larger at the base diameter above the rim. I've had no issues with .38-55 brass in mine. But mine seems to be an oddball at 9.5mm, so maybe it's different than those that are 9.3mm?

The rim on the .38-55 brass fits the chamber cut nicely on my gun, so it doesn't need centering like a rebated rim might.

They're a very strong action. I wouldn't hotrod them to push maximum loads. But no issue with a load leaving the barrel under 1500 fps. 
The little #2 Rolling Block is even smaller and they were chambered in cartridges like .38-40 and .32-20, which can be pretty hot in some factory loads.

National Library of Sweden (Kungliga Biblioteket) might be another place to inquire. I got some original Department of Defense reports about 8X58RD chambered rollers there. Often material one might expect to find elsewhere in Sweden has been moved to KB, which happened with reports I got. 

Best with such old, Swedish only reports if correspondence is in Swedish, at least in part. Staff in KB are very helpful and English capable, BUT, they usually need some Swedish-language text, names, terminology, etc. to focus their searching. I can probably help.

I would not be surprised if you end up getting referred to Norma, or at least to old loading data for cartridges for which M33 was chambered. Do any USA Husqvarna collectors have old Norma loading manuals, tech info about loads, etc.??

About same time I was seeking data for 8X58RD, I had a few email exchanges with person(s) in Eskilstuna about 8X58RD loads for 8X58RD rollers, however, they were not aware of the Dept of Defense reports I found.Will see IF I still have working email addy(s) or names. Who knows what they might be able to provide.

Here is some info about online seaching in KB collections.
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The Husqvarna Museum had no ammunition information and I never got anything back from Norma. I'm taking the chronograph to the range today so I'll have some data.

Wow, thank you Swede. It will take me a while to get it all translated but I think I pulled out a grooved? heavy bullet, 231 grains, for target shooting and a smooth light bullet, 177 grains, for birds and using 50 to 54 grains of powder (black). The bullets were cast of 95 parts lead, 4 parts tin and 1 part antimony.

As you can tell from the above posts it is most like a "38-55 lite". That will influence my next round of testing. For today I had lighter loads in the 32-40 ballpark to ease into it but with a 196 grain bullet which would fall in between the factory 177 to 231 grains. I used 4 different powders (4227, R7, 4759 and 4198), and 3 5-shot loads with each varying by about .5 grains. The sights are 3 leaves with very fine Vs and a pyramidal front. These sights are not kind to my eyes (I'm scheduled for cataract surgery) but I thought I could get some idea of how it might shoot before I sprang for a tang sight and a globe front like I put on my other 33. The leaves are marked 60, 120, and 180 (meters). Not knowing how it would take to my test loads I opted for 50 yards and the 60 meter leaf. As it turned out this barely worked as it was shooting 8 to 12 inches high at this distance for most of the loads. I'm glad I took the chrono as it showed extreme ES for some of the powders which I will attribute to too light loads not allowing them to burn consistently. It also showed that the high ends of some of the loads, say those few that popped up in the 1400-1450 fps range were getting much closer to the point of aim. I'm going to guess that the sights will be on at 1500 to 1600 fps. However, all of today's loads were much slower.  The only powder that was happy with this was good old 4759 all three of its loads (avg fps of 986, 1006 and 1034) were consistent on the target, but 9 inches high, and the last put 3 shots in a cloverleaf and the other 2 opened the group to 1.1 inch.