maybe I've watched too many movies but isn't that what any/every good lawyer does? Client should never speak to the LE unless they're being detained? Like I'm not seeing a situation where the lawyer would tell his client to continue talking to LE.
Retaining a lawyer is never a bad idea, and it's generally recommended on here by people who are involved in the criminal justice field.
"Not cooperating" is another kettle of fish IMO. If your wife was simply missing, there's nothing lost by cooperating. If you haven't done anything to her then allowing access to her life and your life together within the bounds of the law (what the lawyer is there to ensure) isn't going to hurt you.