If you try to send blood samples from Canada to the US, you can end up having problems with US Customs, as they have decided that bovine blood is a potentially hazardous product. If you are sending them to AgriGenomics in IL, you can get a release form that allows you to ship blood by mail, however, in typical bureaucratic fashion, the form is about 3 pages in length and is hard to attach to any package containing the blood samples.
You can now get TH testing done in Canada by Igenity and they can do the test with either hair or blood samples. Most breed association offices in Canada should be able to supply you with more information and forms for sending in samples.
As far as having samples go bad in shipment, I have never had any problems, even with one set of samples that was held up in US Customs for over 2 weeks.