You will need to contact Koodo AFTER the transfer so that they refund you for the remaining days in your billing cycle. Even Bhell, who supposedly have the worst customer service of all providers in Canada, refunds you automatically because that is what the Wireless Code, i.e. the law, says. Koodo (TELUS) is above the law apparently.
Definitely don't cancel first, LD, because then your number will be cancelled as well and you can't port it any longer. Your line will be cancelled when you port out, and you will receive one final bill with the remainder of your tab (if you have any left).