You probably know that this isn't legal in The Netherlands. The receiver of the package can get into problems as well. Futhermore, it's a long journey and you don't know where the package gets possitioned and what the temperatures and oxygen levels will be. I can only recommend to send eggs overseas. You position some wet paper towel inside of a DVD-case, in which you can put the eggs. Put the case a bubble mailer. Sending them in water always results in faillure.
In case you're going to send live animals anyway I would suggest to put them in a sturdy plastic container with some air holes in it. Fill it with wet paper towel. Make sure the container is not too big, because they don't need extra space to get tossed around in. Wrap the container in paper. I wouldn't recommend sending animals aquatic, except when it comes to axolotls and such. I've seen them being send in plastic bags in plastic containers. I don't know anymore details though. Still I wouldn't recommend sending live animals to the US, but since I can't control other people I give this info for the sake of the animals.
When it comes to the other way around (when animals are being send to you) the risk of being "caught" is realistic. I know several cases myself, including one of my mates. It costed him a descent amount of money.