In Switzerland guns are mostly long guns that are heavily regulated and are under very tight storage restrictions. In the US guns are mostly hand guns that are unregulated and under no very tight storage restrictions.
So if you want to make an argument from Switzerland, it would necessarily be of the form: "To reduce gun deaths in the US we should pretty much eliminate handgun ownership and require that all long guns be stored under lock and key in a specified manner, only to taken out on state-permitted occasions for military use."
Your implication is incorrect. One point does not dissolve a correlation. 0 guns -> 0 gun deaths. N guns -> M gun deaths, therefore positive correlation. QED. Switzerland is an outlier in many metrics. They probably don't shoot as many of themselves because they tend to care a bit more about the well-being of their communities. Far fewer people feel the desperate need to lash out against their community.
Some communities in Switzerland actually offer somewhere to keep the bullets in the town hall instead of at home, reducing accidental deaths.
Thats incorrect, see switzerland, they have a lot of guns there, maybe even more than america per person but their gun deaths are very low.