Mailchimp (or Mandrill if you want the API backend) is free for first 12k emails per month. If you are only sending it once, it shouldnt be an issue.
Better to use that then SendGrid since it'll less likely to hit spam folders.
It does sound a bit like spam since this will go to every single email account that has mailed you or you have mailed before. Would it be better to just use Facebook / Twitter / Linkedin + email ~200-300 people.
I on occasion respond to cold emails and on occasion send them. My guidelines:
1. Non click-baity descriptive subject line
2. The person should add their full name and contact information
3. The email should address the recipient by name
4. There must be something in the email that is genuinely personalized
As a recipient, I won't respond unless these 4 conditions are met. As a sender, I won't send unless these 4 conditions are met AND I genuinely understand the customers likely problem and have a relevant solution.
It sounds like your strongest suit might be digital marketing with a data & analytics bent. What about looking at growth hacker type jobs at startups here. I personally hate the term but it seems to describe your unique skill sets (marketing + data science + product design + business skills)