I'm using bias-ply tube tires with no tubes on my original and freshly powder coated 1951 16x4" wheels. They hold pressure just fine. Tire shop didn't see a reason they wouldn't work, even said if they leaked they'd use a sealant on them. I do have metal valves with a nut and seal on them but the guy said the rubber ones would also seal up.
I've used Dobbs in the past. They mounted my last pair of actual tubeless bias-plys on the same original rims.