I believe you can’t change the client on an already created invoice, but you can add yourself (with your own email address) as a contact to that client. Then update the invoice, make sure you (and only you) are set as a send-to contact for that invoice. After you have sent and verified your mail, update invoice back to the real contacts and send again. Make sure to select “Initial Email” in the send dialog (top, center of the window).
We had the same issue when modifying one of the default templates. Our simple way was to create a fictitious client account and apply the modded template to this account with our email address. That way we could make multiple changes, send dozens of emails until we were perfectly happy the template looked pixel perfect. Finally, we changed it to the default template for all customers.