OOPS, I see the rifle is a .357 so you do not want too hard of a boolit, you are going to need a little expansion and a boolit heavy enough for penetration.
Softer lead will need a gas check. Air cooled WW metal might work but you can add a little pure to the WW metal.
I don't hunt with those small calibers but I do know any bullet choice with the .357 is VERY important.