The wheel O-rings are easy enough to find on Amazon or Ebay.
I wouldn't fool with tubes, that's a step backwards. I certainly wouldn't with old leaky tires, because it feels like a waste of money and time. Old, dry rotted tires get punctures more easily and having to break the tire down to patch a tube would get old, quick.
Besides, those rear OHSTU tires are an original ATC brand, may even be original to that trike. I don't know, hopefully someone who's more knowledgeable on the stock tires will say. If they'll hold air, even if needing a tube, and they're not completely shot, they're worth something, if only for nostalgia. If they have any value left, I wouldn't spend it finishing them off.
The Chen Shin C829 is a good tire choice. They ride smooth, are dimpled knobbies which increases traction, and if not ran any higher than 2.5psi they wear really even across the majority of the tread and not just the center like some less flexible tires will. They will look like they're low all the time with the correct pressure, on a heavier 200ES anyway, which may be about 80-100lbs heavier than your 200.
I've read some specs that say they're radial while others list them as bias ply. No mention of radial on the tire itself and the CST website doesn't specify either. I've used some sure enough radial tires before and the C829 seems like it rides as smooth as one, but I can't confirm.
Good tires though. Not the lowest priced, but will last a long time and ride smooth while doing it.
The story of three wheels and a man...