Yes, it will work. Yes, it is safe. .32 ACP is Semi-rimmed, not rimless. The .32 ACP operates at about the same pressure level as the .32 H&R. Depending on firing pin length you may get some mis-fires as the rim is slightly thinner than the rimmed .32 cartridges have.
So far as bullet diameter, it depends. Depending on where the .32 ACP gun or ammunition were made, the groove diameter can vary from .308 to .312 for both. European manufacture tends to the .308-.309, where U.S. manufacture generally runs .311-.312.
With jacketed bullets accuracy does not generally suffer from slightly under-sized bullets, .001-.003, especially in revolvers which generally have slightly smaller bores and deeper grooves than rifles and semi-automatic handguns.