While the British designation for the cartridge (.38 S&W) was .38-200 as a result of original testing being done with 200 gr. bullets, the bullet weight finally settled on for service ammunition for the cartridge was 160 grains. It is a common misconception that a 200 gr. bullet was used! Any 158-160 gr. round nose bullet for .38 Special will do quite well. Other SWC bullets will be fine too, unless you want a bullet shaped like the military load.

Before settling on a .363 bullet try slugging the throats in the cylinder. There is no reason to use bullets larger than the throats if they are smaller than the bore.