Well, first thing I'd suggest is looking online for 7.62x38R ammo and buying it bulk that way. Failing that, you CAN fire .32 HR Magnum and .32 S&W Long with the factory cylinder. If you use .32 HR or .32 SW L expect for some if not all of the brass to be bulged in the middle (in my experience the .32 S&W L is alot less likely to bulge). Accuracy with .32 HR was lower then 7.62 Nagant ammo when I ran it through my M1895, the .32 S&W L was nearly as accurate as the "proper" ammunition.
The .32 H&R is hard to find in my area, and when I do run across it, it costs about the same as the 7.62 Nagant ammo. The .32 S&W Long is equally hard to find for me, but ran me only $18.99 for 50 round last time I managed to track down a box.
A third option is to order a .32 ACP cylinder for the Nagant. You can find them pretty readily on the internet, but they cost a good amount (between $60 and $80 last time I looked.)