Breathing shallow does not mean not emptying your lungs. Shallow breathing means just that.
Few divers seem to understand the mechanics of breathing.
Vital capacity: The largest possible amount of air you can expel after taking your deepest possible breath...
Tidal Volume: The amount of breath you breathe in and out on a normal breath...
For most divers, breathing deeply is an attempt to increase your tidal volume and shallow breathing is an attempt to reduce it. Both are flawed in my mind. The former will cause havoc with your buoyancy and the latter will give you a headache. Try to keep your tidal volume normal.
You can easily control your buoyancy by adjusting your tidal volume to occur with either your lungs fuller or emptier. Breathing on the "top" of your lungs, close to your max vital capacity, will cause you to be lighter. On the other hand, breathing on the "bottom" of your lungs, close to your minimum vital capacity, will cause you to be heavier and of course, you will be deeper as well.
You can leverage this, albeit with a bit of effort and a learning curve, by adjusting when you pause your breathing. IE, pausing with your lungs empty, rather than full will allow you be deeper. Of course, almost all of us pause just after we inhale. We feel safer with a lung full of air. So it takes a bit of practice to get used to it. As a caveat, you must always be certain to only use your chest and diaphragm to pause: NEVER OCCLUDE YOUR AIRWAY by using your glottis. That means that you have to keep it open. That's the muscle you use to say "uh-oh". Ascending with a closed glottis can cause injury or death. Keep it open!!!
Finally, in shape or out of shape, getting rid of CO2 is compromised with depth. Try to avoid creating it in the first place and you won't have to worry about it. Get in control of your trim & buoyancy, go slow and learn the five "Ds" of currents: Dodge, Duck, Dip, Dive and Dodge.
This isn't hard if you approach it methodically. I often dive without a bladder, using only these techniques. I breathe normally in regards to my tidal volume. I simply choose to move that tidal volume upper or lower in regards to my vital capacity to control my buoyancy. Hey, it's how I learned to do it back in 1969. The physics haven't changed since then.