@Metchosinite -- since the E-mails have been "forwarded", they are now stored by GMail, until you delete them.
Did you setup "automatic forwarding", such that every message to your Shaw ID was instantly forwarded to your GMail ID, or have you manually forwarded specific messages? In the latter case, the original message is not "touched".
If your Shaw E-mail was configured to use the "POP" (Post Office Protocol), not the "IMAP" protocol, all your messages currently are stored on your computer.
POP is like taking all the letters that Canada Post stuffed into your exterior mailbox, and bringing them into your home. It's up to each occupant to sort through the pile of letters, and take the ones that are "theirs" into their own room. IMAP is every occupant of your home "peeking" into the exterior mailbox, and then taking "their" messages, and leaving the other messages in the mailbox. So, if your E-mail program is using IMAP, that "mailbox" could be very large, but Shaw will delete it, when you cancel.
