You could have the airport security run by private enterprise. The Federal government would have a minimum set of standards and random plainclothes inspectors. These inspectors would periodically try and infiltrate security, and if successful at penetrating security, issue a $x fine.

Airports would be free to implement whatever they needed to within the current laws in order to meet said standards.

People seem to conflate 'free markets' with 'freedom to do anything they want'. In reality, effective markets are done under a strict rule of law. Set the rules in place, enforce the rules, and let people innovate the best way to operate within those rules. If one airport decides on strip searches and another on random checks then people can decide for themselves (to a limited extent if there is only one airport) which airports they wish to use.

This works for everything from vehicle standards to building standards to food standards - I can't think of a reason why it wouldn't work with security standards.

There would be problems with this system, but it at least has the advantage of not expanding government powers and creating yet another state police force.