Not that this will change your opinion, but Switzerland is not that great of an example to support your "fact" (and even if it was - a few outliers don't prove the lack of an correlation).

For starters it has fairly strict gun laws (essentially no carry permits, gun safes, etc.).

Second the reason for the high gun ownership is the mandatory military service (no standing army) - you can purchase your service weapon at the end of your service period. And for the service weapon the ammunition is stored at the armory - not at home. And without ammunition I would think killing someone with a gun is much more difficult.