I sell to the US and have gotten mostly positive reactions using Giulio's framework. It also depends on the industry you sell to. I call a lot of blue collar workers and they appreciate the direct approach with some humor added. But if you are selling to HR leaders for example they will require a more buttoned up approach.

There are many good openers to use, I'd recommend find a few that sound the most natural to you. Everyone has a different voice and personality and it's better to deliver an opener that you are confident in and sound natural saying as opposed to the best LinkedIn opener that sounds robotic when you say it. Find an opener that you feel good about and track the success rate over your next 50 connects. If you get past the opener 35+ times out of 50 I'd say stick with it. By the end you will have delivered it so many times you'll no longer feel like a "script reader"

I go with the classic "we don't know each other. If I told you this was a sales call would you hang up now or let me have 30 seconds and then decide" This opener has gotten me through to the pitch 80% of the time so far this year. I'll keep using it until it no longer works

@Cinzia Sirbu I call to small business owners. I've noticed it resonates best with the blue collar industries: auto repair shops, pest control, etc. It does not land as well with more serious industries like law firms. For those I've learned it's better to take a more straightforward approach

Giulio has a good resource on it in his cold calling wiki: https://coldcallingwiki.com/docs/objections-wiki/

Instead of saying their name, I simply say "Good morning/afternoon, if I told you this was a sales call would you hang up now or let me have 30 seconds and then decide?"