R-P is "Remington-Peters," adopted as a Remington cartridge headstamp in the early 1960s, and used for all calibers. There is a rifle-only .32-20 round which has not been made in many years. Those used lighter jacketed hollow-point bullets. Any .32-20 cartridges having lead bullets are safe for revolver use. Reloading is the best way to go for .32-20 revolver and/or rifle owners. As you point out, .32-20 ammo is not easily found and is expensive. It's available from internet sources, but shipping cost can be a killer if you only want a box or two.
Post some pictures of your revolver and a SN, and you will learn all about it. Both Colt and S&W quit selling .32-20 revolvers before WWII, so yours is older than that..32-20 is the same as .32 Winchester and .32 WCF. If yours has the barrel stamped .32 W.C.F., it would date from between the mid-teens to the early 1920s.