The extra information you provided was very helpful. It is good news that he was negative for heart worm and his blood tests were normal. It is good that you have been monitoring Cody so closely and working on tests to get to the bottom of this, coughing excessively can indicate a number of underlying diseases not to mention being uncomfortable for Cody and disruptive to the household. The most likely causes of coughing in older small breed dogs are collapsing trachea, tracheitis/bronchitis due to infection or allergies, heart disease and sometimes some tumors. While taking care of Codys dental cleaning is important it is very unlikely that the cough would be "due to him choking on plaque". Because a dental cleaning requires general anesthesia, which can exacerbate heart and respiratory tract disease it is most important to reach a diagnosis that explains the coughing and attempt treatments and hopefully see improvement before any dental cleaning is done.
It is great that you have done a lot of testing on Cody already. It is worth considering an electrocardiogram to assess his heart rhythm. Because a lot of the problems that I mentioned can be diagnosed on x-rays it is very important to have a veterinarian review the x-rays. There are subtle findings that a human doctor may not be familiar with. Either you could show the x-rays to your veterinarian I think taking Cody to see a veterinary internal medicine specialist would be an even better step since the vets he has seen already have not yet been able to reduce his coughing yet.
I realize that a visit with a veterinary internal medicine specialist can seem a bit daunting but they are in the best position to use their advanced training to diagnose problems quickly. They are also able to tell you what tests they think will be most helpful so you can avoid spending money on less useful tests. They also will be able to discuss the options of medication trials with you, there are other medical options for treating collapsing trachea and allergies. A specialist will be able to start Cody on treatment at the right dose and guide you on when to make a decision if a trial is effective or not. It is great that you tried benadryl but it is often not effective for coughing.
Steps that a specialist may suggest are: have x-rays repeated and reviewed by a board certified radiologist, perform an EKG, use fluoroscopy (a moving x-ray) or scope.
I suggest that you have the specialist review the x-rays you already have then follow their suggestions step by step. Also have the specialist confirm that it is safe for Cody to undergo general anesthesia before doing a dental cleaning.
I realize that it can be frustrating to deal with chronic coughing in an older dog but the good news is that with advanced training and tools internal medicine specialists are much better able to diagnose and treat coughing effectively, and depending on Cody's final diagnosis there are often range of good medication options available.
Please let me know if you have any other questions. I wish you and Cody the best of luck.