You may very well be correct. I found your photo in "Polizei greift ein" and the others seem to show both methods of carrying the sword. Since most of these troopers are wearing greatcoats it is difficult to tell as you say. The issue sabres were so darn heavy, I would want to get it on my saddle and off my hip when I was mounted. I just can't tell which swords they are carrying.
Here is a shot of the reverse of the heavy sabre that you show. The same "1920" marking on the obverse guard as yours and police markings to the Schutzpolizei Liegnitz on the reverse.
