Agree entirely, that's definitely velvet you describe. You may not see spots anywhere or other symptoms. The swimming in to powerheads and quick death thereafter is key.
Many wrasse can actually build a resistance to velvet and ich. My wrasse tank actually has had velvet and ich for 1-2 years, but no one succombs because other than a blonde naso who is tough as nails and now immune/resistant, the rest of the fish are wrasse. I lost two wrasse to velvet early on and then everyone pulled through.
With wrasse I suspect that it is the slime cocoons they sleep in that protect them, and for sand burrowing wrasses I suspect the fact that they're hiding under the sand also keeps the parasite from taking over while they build an immunity/resistance.
The only reason my fat blonde naso is so hardy is that she was a Petco fish. She was subjected to velvet and ich for months before I bought her. I knew that a wrasse from a vendor on here brought velvet (that wrasse survived and we later found out that vendor had given velvet to many users here -- that vendor is no longer with us) also. A visual inspection of her at Petco showed that she had steadily improved through months of suffering. She's now very hardy and I've never seen a spot on her since I've had her (again two years)
To the casual reader, please understand that this is NOT normal and NOT ethical. Although some wrasse CAN survive ich and velvet they shouldn't be expected to -- nor is it fair to subject them to this as many will die and few people have the system stability, water parameters, and the "plan b" if things go awry. I still lost two wrasse and had my quarantine not been full of tangs with velvet at the time I would have qt'd everyone.
Once my 55 gal qt is again empty, I plan to qt and treat all of the inhabitants in the 125 wrasse tank with velvet because it's the right thing to do and I can then add new fish to this tank again, which I haven't done since discovering this. Things appear fine but this is not how I wish to run my tank long term.
Anyway, my point is that your wrasse may never show symptoms (especially since your tang apparently didn't show outward symptoms like dusting or spots) but absolutely will infect your tank.
I've cross contaminated both of my other 180 gallon reef tanks with ich AND velvet by simply sticking my hand in my velvet/ich management tank in to one of them (to put nori in, dumping skimmers, sharing nets, drainage hoses for water changes, etc). So a fish host is a steadfast guarantee of adding velvet to your DT. Don't risk it. Treat with copper or CP