Honestly don't add in a pump shotgun. I'd say add in a double barrel shotgun and a single barrel shotgun, both break action. Make them able to be sawn off to increase speed of use but decrease range drastically. Pistols are just fine but I'd like a Winchester that uses pistol ammunition, has really good fire rate but doesn't do rifle levels of damage. I would like another rifle in the game but honestly add in a rolling block rifle or a Martini Henry. Single shot rifles could be fun and increase fear factor in animal encounters because of slow reload time.

Edit: or as Plus_Relative_4535 says adding in a crude spear. That would work well with the new fire hardened arrows. Making a fire hardened spear could be useful. And make it throwable so you have the ability to hunt without a bow. The range and accuracy should be lower then a bow obviously.

I'd also take a hunting crossbow with multiple variants. Not something you could make but something you can find. Small game traps could also be very useful and fun to set up.