I would
I would disassemble the chair as much as possible - especially disengaging the backrest from the seat, since that is where it is most vulnerable. I'd also get some thick polystyrene foam and wrap the edges of the plywood. A good crack to the edge of the ply can be a nasty piece to glue back together.
Disassembling is fairly simple: If you slide your fingers between the cushions and the wood you should find a snap at the bottom of each cushion. Pop that up, then slide the cushions up and off their clips. Then its just a matter of locating the screws that hold the backrest onto the seat.
Very serious collectors...
Very serious collectors would like to receive their items assembled and untouched, but of course that adds to the shipping cost. Especially with old pieces, you may risk damaging the hardware since they might be rusty and unwilling to cooperate with the dis-assembly process. On the other hand, shipping a large item like the 670/671 assembled has its own risk too because it'd be more susceptible to damage during shipment unless you have a reliable delivery company working for you. I've shipped parts of the 670 both domestic and international. The biggest part probably is the seat panel (and cushions) and when you have the right box, you should be able to fit the top and lower back panels as well.
Good rule of thumb for domestic: USPS is the cheapest although they have a size limit. Fed Ex is generally cheaper than UPS and neither of them has a size limit as long as you have the right box.
For international: forget about Fed Ex or UPS. I once got a quote of $300 for shipping a 670 base to France. But then again, USPS has a size limit.
Hope it helps.
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