In addition to what @rosemarythyme already wrote, your piece is going to be outdoors so there is no chance for the aromatics to build up. They will simply dissipate as the piece continues to off-gas. That is why it smelled so strongly when you first opened the box. The aromatics were trapped inside the container.Ought to be OK, from what everybody's saying.
I don't have any cedar lumber but would not hesitate to use an aged piece outdoors should the desire arise.