Can you hire a plumber and electrician without going through the contractor?

My first contractor flaked out and never gave me an estimate after I spent hours explaining to the plumber and electrician what I wanted done. Now I am trying to get the plumber and electrician's estimates and have them lined up to work on a specific date. "Professional courtesy" because the bid was under the flakey contractor has impeded the process. I want to save the "surcharge" my contractor would charge and just hire the plumber and electrician by myself. Why is this so hard? What is the secret code to get this done??!! I want to save myself the money, especially since the bids are already done and they know what I want/need done!