I think you have many variables
1 - transport. Some airlines might be a total pain - their enforcement is likely to be strict.
Your best solution here might be mailing the stuff home - the post office generally doesn't care. As long as its not a white powder....
2 - the type of wood. Best to check CITES for whats controlled. Keep in mind that a lot of this is very loosely enforced. Worst case, it gets impounded and you loose the shipment.
However, please don't interpret me as justifying the purchase of endangered species.
There are some absolutely spectacular types of wood in central and south America.
Costa Rica and Honduras has some gorgeous very dark, oily woods. Guanacaste is awesome, but controlled/endangered. You can buy wood from trees that have died naturally.
Venezuela had purpleheart logs that were huge and fantastic
You can buy anything there...but you might want to avoid that country right now...
Importing any of these might be a challenge due to CITES.
We've travelled a lot around central America and checked out a few woodturning shops.
Generally spectacular wood, but workmanship is mediocre
For a while, my wife wanted to move to Curacao, which has almost no wood.
So I'd have to import everything. Venezuela was my top pick.
For now, we're stuck in Canada and I'm stuck with much less exotic maple.
And its cold!