I'm not sure how south you're looking at going, but Hunt Club Rd will bypass most of the city and has ample bike lanes for most of its length. If you're looking to head straight for the river, I'd suggest heading north from Kanata instead of going way out to Stittsville. Eagleson Rd/March Rd is the main north/south road in Kanata. March Rd (north of highway 417) has ample bike lanes through the populated parts but will drop down to a two-laned road once you get past the northern part of Kanata (and in suburban style, it'll be blatent). Turn onto Dunrobin Rd and it'll eventually lead you to the rier. If you're set on going to Stittsville, Carp Rd will be the most direct route to the river, though it can be busy at times. It's mostly farming outside of the city and the roads are pretty easy to follow. Poke around Google Maps and take a look at a few sideroads.
Feel free to message me if you have any questions. I've lived in the Kanata area all my life and know the area pretty well.