Which protein sources have the lower carbon footprint
The lowest - actually, negative carbon footprint will be plant proteins - like legumes: beans, soy, lentil. (organically grown plants, produced without artificial fertilizer or heavy farming machinery break down more of CO2 than processing them afterwards creates.) To reduce it further you might pick up gardening and grow your own, organically - even the organic farming market has a bit of carbon footprint (cars bringing the foods, maintenance of the market, all the industry behind bureaucracy required, etc) but if you use simple hand tools, and grow a small plot by your house, the carbon footprint will be firmly in the negatives.

You may want to look at the source of your soy though. The fields are often replacing large swaths of the amazon forest. That would be heavily counter-productive. Other legumes don't require that sort of climate, so they have a lower impact on the environment.

The "leftovers" protein sources as you put it are actually a good choice too. They have a pretty large carbon footprint, but the problem is that this carbon footprint will exist whether you buy (provide demand, so incentive for production) or not - they will "happen" as byproduct of the main production regardless of demand, and the CO2 will be produced regardless of whether they are going to be sold, or just discarded (or redirected to animal feeder.)