Seems to me that the Help Page for DNA Confirmation is pretty clear:
"It's also recommended that at least one of the test takers enter their DNA test on WikiTree, and set their profile's privacy level as Private with a Public Family Tree or higher."
Where I come from, "recommended" means one thing, and "required" means another.
So, NO, the test takers do NOT both need to be WikiTree members, although that would certainly be great! In fact, what this says is that it's literally still OK if NEITHER are WikiTree members.
Your REAL problem is that NO, a half-3rd cousin does NOT qualify as a "third cousin or closer" required to avoid the need for triangulation.
But you're IN LUCK!! While this person is YOUR half-3C, they are a half-2nd cousin, once removed, to your DAD! Since half-2C1Rs share the same amount of DNA, on average, as a 3C, I'd say you can use your DAD's test to perform that confirmation! Half-2C1R is "third cousin or closer", in my humble opinion (I haven't heard of any formal rules on this).
Like I said, NEITHER test taker has to be a WikiTree member, so you don't even have to talk your dad into a free practically-anonymous membership to do this.
As far as how to "document the non-member(s) in the confirmation statement", the instructions are kind of self-contradictory, so you just need to apply the spirit of what they're trying to get at. One the one hand, you need to say who they are; on the other hand you can't say who they are if they're living (which they almost always are right now)! So they say you can just use their initials.
I'm hoping to get doing my confirmations in this month, myself! I'm also trying to pick a triangulation I can attempt - I'll probably have to beg some people to get on GEDmatch for that. There's a tricky move I figured out to get six of my gt-gt-gt grandparents confirmed without triangulating, plus I can do 14 out of 16 of my gt-gt grandparents the normal way, (given my revelations here). For my last two gt-gt grandparents, there ARE no 3rd cousins, for the one - and there are very few (if any) 4th cousins, and none are known to have tested - and for the other it looks like there are NO 4th cousins at all!
Good luck!!