"Sticky mitts" doesn't sound jarringly British to me. I think you're generally okay there. Though you may want to consider the expression "paws" or "sticky fingers". You're right, braid does sound better than plait for a Canadian accent.
Some other words you might want to avoid:
whilst (use while)
nappy (use diaper)
lift (use elevator)
I can't remember what you guys use for washcloth and facecloth, though I remember once reading a story where it really stuck out. A washcloth is for dishes and things; a facecloth is for the face and body.
basin (use sink)
fancy (use to like or something similar) - unless you mean something like "really fancy clothes"
brilliant! (use "cool" or something - unless you mean really smart, like "a brilliant scientist" or "a brilliant idea")
sack (use bag, unless it's a feed sack or something big and industrial, like a burlap sack for potatoes)
I'm trying to think of some words or expressions that would be considered uniquely Canadian that you could use to sprinkle your dialogue, but my thoughts are failing me here. It's hard to peg exactly what characterizes your own accent, after all. (It was weird, when I went down to New Mexico, being 'the one with the accent'). There's certain things like Saskatoon berries and caribou and inukshuks and poutine and Tim Hortons coffee and so on but you'd have to create a context for them. There are also regional differences in Canada - a hooded sweatshirt with a pocket, for example, is a bunnyhug in most of Saskatchewan (and always will be! long live the bunnyhug!) and some other areas, but it's also called a 'hoodie'.
Of course, there are two major stereotypes of Canadian English, one being "eh?" at the end of sentences, and the other being "aboot". The latter refers to something called "Canadian raising" which is a particular quality to the diphthongs. Not every part of Canada does it, though I know a couple of people who do it really strongly. I only hear the 'eh' once in awhile and usually (in my area at least) it seems to be characteristic of the local Aboriginal accent. People have caught me at it once or twice, though I really try to avoid the stereotype (I say 'hey', not 'eh'). For the *most* part, in terms of our wording anyway, we sound like Americans. Polite Americans. (Ducking the items hurled at my head). :D :D
My advice is, do what you can, listen to McKay speak onscreen as much as you can to get 'his' voice, then get a Canadian beta to read your work over. It's easier than trying to remember everything!
Oh, and just as a side note - Rodney's comment about climbing ropes and "Participaction" in Vengeance was for me the only redeeming thing about that whole ridiculous episode. I laughed and laughed. Total Canadian nod.
And on one final unrelated note: I heard somewhere that British people will not eat Saskatoon berries because they don't think they're edible (literally or figuratively, I'm not sure). Is that true?