The short answer: bird and trout knives.
Small game can be even more challenging to dress out than large game. Consequently, makers build what are called bird and trout knives, which generally feature thin, slender blades 3 to 3.5 inches long. You can find such knives with both drop-point and skinner-style blades.
The blade is primarily designed for the tasks of dressing out birds and fish, hence the name. Birds are generally dressed out to harvest the breast meat. Fish are dressed to get the fillets. (Most hunters and fishermen discard the remainder of the bird and fish.)
While a fillet knife may be the better choice for dressing out fish, you then must carry two knives.
The other choice is a folder with a 2.5-to-3-inch blade. Some feature a blade and a gut hook. As this implies, the idea is to insert the hook into the bird or other small game to pull out the intestines and the rest of the intestinal tract.
Generally, the ideal bird-and-trout folder has either a 2.75-inch drop-point blade or is a multi-blade with 2.25- or 2.75-inch blades featuring a combination of a skinner and a drop point.