Does modifying my weapon view to left-handed change how other players see me?

Solution 1:

No it does not change how others see you.

However, it will change everyone for you.

If you're viewing yourself as left handed, you'll also see everyone else as left handed.

It works the same way for right handedness, everyone else will see you as they see themselves.

The 3rd person character model does not change at all either way.