Boxing won't help you with golf. I took boxing as a kid and I'm glad I did. It helps teach you footwork, endurance and how to throw, take and duck a punch while being a humbling experience. Great for children to learn.
I'd say do yourself a favor and start taking up yoga. I would then work on things to strengthen your lower body (i.e. squats) and your hands, wrists and triceps. Still, I feel flexibility is twice as important (if not more) than pure strength. I don't think there's any real need to get buffed like Tiger. So whatever you do, make sure you're flexible.
I would consider doing something else than running. I used to date a girl who ran cross country, indoor track and outdoor track since she was 12 years old and then ran outdoor track in college and the running did significant damage to her feet and knees over time. Then my father took up jogging every day about 15 years ago and did damage to his knees as well. There's many that say that you just need to learn the proper running technique to prevent injury, but many don't know what that proper technique is (I don't).
Anyway, there's other ways to lose body fat, improve cardio and improve your lower body strength without doing damage to your feet and knees. But again, I think the key is flexibility first, then strength in certain areas (lower arms area, lower body)
3JACK