Japan has a higher per capita rate of suicide than the US does. Japan has essentially no personally owned firearms. Half of all US suicides are effected with guns. Half of all firearms related deaths in the US are suicides. If firearms were to magically disappear from the US, those who want to kill themselves would simply find other means to do so.
I once had a bumper sticker; “If they outlaw guns, can we use swords?” (Member of SCA back then).
England banned guns. Now, with some high profile murders with swords, they are thinking of banning swords ... and long knives, and bats ...
why not just ban murderers and dispose of them? It would be easier.
Some years back I read a report that when Canada (or some Canadian city) banned handguns in an attempt to lower handgun suicides, the rate actually fell.
However, the rate of suicide by bridge-jumping went up, so that the overall suicide rate stayed the same.