Can I choose to not register my child as a US citizen?
No. Your child will be a US citizen regardless of whether you register anything, and (unless you have spent less than 5 years in the US, or less than 2 years after you turned 14) regardless of the place of birth, because (in that case) even if the child is born outside the US he or she will be a US citizen under 8 USC 1401(g).
Can I register them with an 18yoa deadline for them to choose citizenship?
No. Your child probably (depending on your wife's citizenship, and assuming birth in the US) will be a dual citizen from birth without the need or the ability to choose. On turning 18, the child will be able to renounce either citizenship, but will not be required to renounce US citizenship and will probably not be required to renounce the other citizenship either.
(I am not familiar with all EU countries' citizenship laws, so the law of that country might have a requirement to choose, but there is no such requirement in the countries whose laws I am familiar with. If the other country is the Netherlands, the child will risk losing Dutch citizenship on turning 28 unless he or she takes steps to avoid that or unless the law changes.)
As pointed out in a comment on Putvi's answer, if you successfully avoid letting the US know about your child's birth, you would be in the awkward position of needing to get a visa for the child if you ever want the child to leave and reenter the country. Otherwise, the child would be an illegal alien in the eyes of the US (this assumes you've managed to hide the child's place of birth). There is no process available to get visas in the US for (non-diplomatic) children born in the US, of course, because such children are citizens of the US.
