Small employers hiring around Raleigh, insurance claims processor here

Two small Raleigh employers told me they are hiring but have not posted yet. There are 6 people counting on me, so I am trying to be careful. They like a brief email with a résumé. What do you write in a cold email?

Keep a list of who you contacted and when. It makes follow-ups easy.

A short email with two sentences about what you can do and your résumé attached worked for me. I followed up after a week.