I don't see how it "runs the risk giving your voting choice away" more if you vote in advance, than it would on election day.
It's the same voter information card we hand over to them in either case, that lists a poll number for both the election day and advanced days (and not just "the, er, "postcode" of whomever does the voting").
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They then draw a line through your name on the list they have in front of them. You're on the list of voters prior to the election, before you or they know if you're going to vote in advance of election day.
I don't see how or why they somehow have to record voter data differently for advanced voting (if this is indeed what they do) than on election day.
Information on the voter information card for the 2025 federal election in Canada.
www.elections.ca