I don’t think it is that simple to void a contract entered into by an agency of the government, even if you are POTUS.
Agencies have to follow their own rules of procedure or be subject to litigation. That is why the pace of deregulation isn’t faster. (They have to hold hearings, etc.)
It’s probably easier for President Trump to cancel an EO of President Zero than to abrogate contract entered by an agency (or perhaps the Pentagon), especially if he is likely to face DS opposition.
I think an order to the agency head from the President would perfectly legally void an NDA. There are laws about what is and what is not confidential, and the President can declassify anything he wants, just as he can allow the release of information that an agency previously wanted to keep secret under an NDA.