It already works in your situation. And it triggers every time you swap weapon.
No need to get duplicate weapons just to trigger a sigil.
Even if you were to put a dagger in your main hand, and the only other weapon in the other weapon sets offhand slot, you would be wearing both all the time AND trigger their weapon-swap sigils.
Just for informative purposes: Even other things can trigger weapon swap sigils (or traits for that matter).
E.g. going in and out of your Celestial Avatar as a Druid, switching kits on your Engineer, elements, shrouds, tomes... see the wiki page for more.