I'm not sure yet. They're still working on the details, which should include testing sites they'll accept. My first preference is definitely to do a mouth or nose self-swab, next would be a mouth swab by them, then shallow nose swab by them. I'll avoid the invasive nasal swab if at all possible.
Do not take these nasal swab tests. We do not know what is on, or in these swabs, or what they may leave behind after a test. They are no different than the vaccine in that they are penetrating your body with unknown variables. Just watch the first minute or two of the video below to get an idea of what you might be subjecting yourself to.