I would not personally invest in a deckchair, though they might be useful for rams, for doing their feet and applying raddle. I would think you would want to get the sheep crammed up whilst you are trying to get them into the chair.
If I wanted a tipping crate I would probably make one. If you look at one and make a few sketches and measurements I think it shouldn't be difficult if you can weld or even get someone to weld it for you.
I know an old man who has about 100 ewes which he shears himself using a tipping crate. He does about 3 or 4 in an afternoon whilst listening to the radio. Then tomorrow afternoon he will do 3 or 4 more if he's in the mood. It takes him about a month to shear them all and they wouldn't win prizes, but what the hay.
The hardest trick to shearing is holding the sheep I think. He uses electric shears, the type with the motor in the handset.