Getting used to a certain knife or type of knife is a good point..... I got used to using traditional knives and used them for years for both small and medium sized game. I honestly had little need for a fixed blade, but I see the utility of one for the woods. I carry one now and it varies. If I were hunting whitetails today, I would carry both a traditional folder and a small fixed blade such as you mentioned. Dozier's come to mind, but I have a lot of choices available. I have cut myself cleaning out the heart-lung area in the woods where you are going pretty much by feel. But never big injuries. A locking blade is not necessary and cleaning a folder is no big thing.
The problem is unless you feel pain from a knife injury, there is so much blood around that you are not likely to even notice the bleeding cut until you clean up afterwards and you continue to see blood.