H&R 32 break tops that were designed for smokeless powder had the caliber marked on the left side of the barrel (beginning 1905).
I don't believe H&R started offering the 32 S&W Long until post 1905, so you don't have a 32 S&W Long from your description if there are no markings.
A smokeless powder H&R 32 would be marked something along the lines of: "32 CAL. S.& W. CTGE" to indicate a 32 S&W (short) chambering. The cylinder will be about 0.925" long for the 32 S&W (short). For comparison, the 32 S&W Long case length is 0.920" versus a 32 S&W case is just 0.605"
As a rule of thumb, H&R six shot 32s are 32 S&W Long and five shot 32s are designed for 32 S&W (short).
Modern 32 S&W (short) ammo through a break top designed for black powder 32 S&W would certainly be an "at your on risk" thing. I have and occasionally shoot a 1910s 32 S&W H&R break top but I exclusively reload for it and stay with the starting suggested loads.