Your analysis is correct. Selecting print from that preview screen, won't send an email.
Which function are you using to send the email? Generally, the common function module is SO_NEW_DOCUMENT_ATT_SEND_API1
Try using this function module instead: SO_DYNP_DOCUMENT_TRANSFER_API1. This gives you an option to view the email and waits for user input to send the email. I haven't used this function module personally, but it should work.
Thanks,
Juwin