Am I able to sign a contract with my parent's signature if I am under 18?

Under New York law and the law of most states (it is likely but not certain that New York law would apply to this situation), contracts with minors are valid, but they are voidable at the option of minor.  In other words, the other side would be bound, but you would not be because you can void the contract as long as you remain a minor.  Thus, it is not that you cannot sign a contract - you can.  It is that the person or entity with whom you are contracting would not be willing to accept just your signature because they would gain no protection from the agreement.  That is why those employing minors, like modeling agencies, sign contracts with the parents, not the models.  If your parents signed an agreement that you would not disclose trade secrets, that should be valid and binding, but the question is really a practical one - the online business accept your parents' signature?   If so, fine.  If not, you cannot force it to do so.