Hi Caroline,
You're a go-getter. I like that
When you are cold-emailing your prospects I do hope you are contacting people with whom you have a prior relationship. People don't like Spam and that's what cold-emails are. You don't want to start your new business off on the wrong foot. Read the
CanSpam Act for more information about sending unsolicited commercial emails. It's very bad practice.
Anyway, not to put you on a total downer, let's talk about LinkedIn. Effective use of Linked In requires you to answer and ask questions. That is the only way to get yourself noticed.
Regarding what to say: If you have determined your target market then the best way to approach it is to "tell them what you have, how is it going to help them, and what should they do next". No one will buy from you if they don't need what you have. Help them to see that they need you. All Virtual Assistants solve the same problem for their clients no matter who they are and what they do. We save time for our clients and thus give them more time to do what they want. (whatever it is) Our clients don't have the time to do everything and so they look to us to help them do the things they hate doing or the things they don't know how to do and don't want to learn.