In my headcanon of the unrated version Wolf called for backup after finding out aliens were onboard the ship but he decided to try to deal with the aliens while the others were on the way. The skinning part can't be solved that was pointless. At the end the Predalien should have knocked Wolf's mask off instead, none of that homage there, and Wolf should have activated the self-destruct before going melee on the Predalien. Better than the RE2 ending with goverment.
With some fights, the plot demanded Wolf to make mistakes otherwise he would have killed all the aliens on the sewers, and no more movie. Hell if the Predator that shoot the ship was smart he would just self destruct instead of sending a distress call, but then again no more movie.
The whole premise was a mess from the start, why that scout ship even went back to Earth? Several elements of the plot would need to be changed, reason for the ship's crash(no shooting plasma inside on it), Wolf could have been already hunting on Earth and decided to check on the crash, other Predators couldn't arrive on time etc.