If the items are insured for their true value - presumably about 200-250,000 yen then I would be very, very surprised if you managed to escape paying a hefty import tax upon delivery. If your relative claims they are used items valued at 20,000 yen then you might get lucky.
Two things - if they get lost or damaged in transit you're both screwed and then there's the fact your relative has actually made a false statement with the intention of deceiving US customs. I don't know how seriously they take this sort of thing - here in Japan it's very much 'what the eye doesn't see the Devil won't write home about'. When my suppliers are honest I end up paying taxes, when they're not - I laugh all the way to the bank.
Why not try sending the camera first. Value it at 20,000 yen. See what happens.
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