I'll give an opinion (i.e. don't know for sure). I don't think you sister-in-law even has to register the kindle but when you do register, you have to include in the registration a
US addressed credit card. You don't ever have to use that card. All your purchases can be made with gift cards.
As for the gift card, if she sends it to you, then no one else will know where you are, US or Canada or anywhere. So I believe that you only have to worry about the credit card's billing address and some other posters have mentioned a work around for that but I'm not sure what it was. Something about some agencies that will "US" register a card through their company, I think.
Oh & welcome to MR.