Hi there. If you want to collect person's Email, firstly you need to be connected with him/her, otherwise, you can't collect the email using LinkedIn API, you must do the dirty work (scrapping). Just need to state that. What is/would be the "original LinkedIn connection message"? I need some explaining of that term. Will the video be hosted somewhere, or everytime reuploaded for a new user that the message is sent to?
What language would you like to use? Python is generally used for scripting and is easy to understand/manage by any person.
Also, when do you plan to start this project and when is the deadline?