So is there any way to do this?

I think the bard's songs quest has a script to disable music, not sure if dialogue is also affected by it.

Thanks in advance!

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You are not alone in wanting to know if this can be done.
I have been trying to find a way to cut off NPC to Player jabber when I cast a custom teleport spell as if they are jibbering at the player, they get caught in the effect and moved as well.
I had one idiot from the Winking Skeever transport to Sky Haven Temple that way, which was not what I wanted to have happen.
Another time, after reloading and leavingthe inking Skeever, it was a Solitude Guard. Have fun waling home dude.

What we need is a way to make the player "invisible" to Those who initiate dialog.
Toggling the AI for all the actors in the world off and on seems like using atomics when all one needs is a match.

Any ideas, folks?

I might have found a solution.

I reverse engineered a mod and took a peek at it's scripts, and I found that

SoundCategory.mute()

works, where you add Sound Category as a property. There's a MUS property, an AMB property (ambient music?), probably one for dialogue too (I haven't checked all of them.

Hope this may help you too!