Technically, you can enforce your policy whether the person signs or not. Dealing with the aftermath of them claiming they didn't know is a pain, so there are better ways to handle it. Read on.
You can enforce your policy even if you don't notify people. Unfortunately, that could end up resulting in the appearance of discrimination, depending on who is affected by the policy change. You can also expect increased unemployment insurance bills if there's a flood of terminations due to the secret policy.
The best way to handle this is to have a meeting with a witness and inform this person of the policy, inform them that it applies to them whether they sign or not, and ask them if they have any questions and answer any that they may have. Then have the witness sign off that the other employee refused to sign the document but was duly notified of the policy and that it pertained to them and that his or her questions were answered.
In some places, you can tell them they must sign the acknowledgement under penalty of insubordination for failure to do so because they are merely signing acknowledgement of the policy. In other places, that's too aggressive and you would have to talk to your own attorney to get the answer to that one.