No. The licence number stays with the boat. The buyer transfers it within 30 days. The seller should not cancel it.
A Pleasure Craft Licence number is issued to the boat, not to you personally. When you sell, the buyer transfers that same number into their name. Cancelling it leaves the next owner without the number that is already on the bow.
Transport Canada says the buyer must transfer an existing licence within 30 days of the ownership change. BoatHandoff puts that deadline on the bill of sale and, in the full kit, on a checklist with calendar reminders.
Give the buyer the licence document, a bill of sale with both signatures, and enough detail to identify the boat: make, model, colour, HIN if the boat has one, and the licence number.
You still apply for the transfer yourselves on canada.ca. BoatHandoff does not file it, and it is not affiliated with Transport Canada.
The free download covers the proof-of-ownership fields. The full kit adds the walk-through and both signatures.