Since you have a valid H4 visa, I think you can choose between H4 and AP, which one to use. AP is for those who does not have other option to re-enter united states such as expired visa.

But the debate is what will happen later at the renew time? During the initial application, the requirement was that you must be Nepalese Citizen and  must be in united states on or before June 24. So, during the renewal, you just have to give them the same set of documents.

Once you are into parolee status, one has to go back to home country to do the adjustment of status to revert it back into H4. The question is how difficult will it be for the change of status. If your primary applicant, H1 is in the Green Card Process, it would be wise to maintain H4 visa.