The Knives of Alaska Cub is both. IIRC it's actually offered as both a fixed (that would be my preference) and a new folder they've brought to the market.
OK, to address your question I strongly prefer a smallish fixed blade of no more than about 3" in blade length and certainly less than 7" inches overall. I like a thin blade stock, no more than .125", a high hollow grind is my preference, but I wouldn't argue with a thin flat ground blade. Any of the very good blade steels I mentioned above would suit me fine with me probably favoring carbon steels such as 52100, 1095, or the semi-carbon D2 and M2. If "stainless" was my only option S30V would be the choice. I like natural handle materials such as Stag and Jigged Bone, but for a pure working knife Micarta is tops. I like my handles to have a slightly rounded and very slightly curved feel. A single finger groove is alright, but no more than this one. I don't care much for guards. If they're present they must be small, real small. A Kydex sheath takes the worries out of security and clean-up. A horizontal/crossdraw sheath is handiest of all worn to the left of the front belt buckle. The fixed blade is simple, strong, always ready, and the clean-up from blood, fat, hair, ect., is a snap. Much easier than a folder. That's my ideal fur knife. Something like the Dozier Canoe Knife or Arkansas Traveler. There are several other Dozier's that fill the bill very well too. A Scott Cook Small Owyhee Hunter is about perfect as well.
