I tried the kiosk last year and it will only renew your card if it has expired, not the yearly sticker. For those you still have to go to an outlet like Canadian Tire or BPS.
As far as how long it takes for the card to come in the mail, the last time I had to get mine it was about 3 months before it showed up in the mail.
Forgot to mention, it's about a kilometer down river from the locks in Hastings, so if you wanted you could pop into Rice Lake. I found though that the area on the Trent is pretty quiet (and as a result under-fished), no boat raffic except for guys in their yachts coming through from Rice.