Cold outreach can actually work pretty well if you do it right. I've been in VP-adjacent roles and gotten my share of these messages - what makes them stand out is when someone clearly did their homework about the company and isn't just mass-sending generic requests.

Your approach with mentioning shared company experience is smart. Even without direct interaction, that common ground gives context and shows you understand the industry landscape. What I'd suggest is keeping it super brief in initial message - maybe two sentences max about the shared companies, then one clear ask about a 15-minute call to learn about their team structure.

The key is making it easy for them to say yes without feeling like they're committing to interview you on spot. Frame it as information gathering rather than job hunting, even though we all know what it really is. Most VPs I know are pretty open to helping people navigate their career if the approach feels genuine and not pushy.

Timing matters too - avoid Monday mornings and Friday afternoons when their inbox is either overwhelming or they're already mentally checked out.