Pull ups aren't a particularly good pulling exercise either, they have the same effect of pulling your shoulders forward. Any sort of rowing motion, anything you can hang from while being horizontal, resistant band exercises. For external rotation exercises with light weights, cuban presses etc.
Why is anything besides endurance workouts for your muscles important in boxing? Strength exercises aren't actually going to make you faster, increasing the size of fast-twitch fibers won't do anything for a boxer.
Strength training increases your endurance, your motor skills, agility, speed, tendon stiffness etc. Increasing the size and the proportion of your fast twitch fibres is beneficial for every athlete, including elite marathon runners. Tendons are responsible for most of your power, they are like rubber bands so the stiffer they are the more recoil you get after they're stretched. For submaximal movements you are more efficient/economical. The benefits of strength training are endless for athletes, especially the neuromuscular effects. Strength training will absolutely make you faster and more powerful. Read some scientific literature and educate yourself :good
Body exercise daily. Nothing wrong with that. Just don't do the same thing. Change it up. Chins one day, push-ups the next day, abs everyday ???
All I got to say is, remember to keep the balance between your pushing movements and pulling movements. Otherwise you're in trouble.