I can assure you, YOU NEED TO WRAP YOUR HANDS! Same thing with hitting the speed bag. Unless you want battered, bruised ugly hands that look like you've put them in a blender then reassembled them to look like a hand, you should wrap them. That's why they were invented to protect your hands. Ask around a boxing gym and they will tell you the importance including how common it is for boxers to break their hands. I've wrapped my hands since day one. Most people look at my hands and don't think I'm a boxer. I use 20 oz gloves on the heavy bag as well as wraps. After 6 to 7 rounds my knuckles start to hurt. Yet, I can go 12 to 16 rounds in 16oz gloves sparring. My hands hurt less hitting someone than the bag. Not trying to scare you, but give you some sound advice.
Keep your guard up and come out punching.