I learned these exercises some years ago in an exercise class run by a former boxing champion. You need no weights and you don't have to do push ups. And at over 60, I do NOT have "bingo wings".
Stand upright for all of these exercises, knees soft. Work up being able to do 1 minute on each exercise. You may want to start at 20 seconds per exercise first. You can do them in any order.
1. Arms held straight out in front of you at shoulder height, palms facing down. "Paddle" your arms up and down quickly, a distance of about 6 inches in each direction.
2. Arms held out straight in front of you at shoulder height, palms facing. "Clap" your hands, without them actually touching. Keep moving your hands back and fore quickly, in the clapping motion.
3. Arms straight in front at shoulder height, palms facing down. Make a fist with each hand, then straighten your hand out. Again, keep doing this quickly.
4. Arms held straight but now pointing to the ceiling at about 45 degrees. Cross hands over one another in a scissor movement, alternating which hand is on top.
5. Repeat this with hands straight up in the air.
6. Arms straight out to your side at shoulder height. Palms facing down to the floor. Paddle your hands up and down quickly just a small distance.
7. Arms out to your side at shoulder height, palms facing front. Rotate your whole arm in a small circle, as if your fingers were outlining a cricket or tennis ball.
8. Repeat in the opposite direction.
If you can do all 8 exercises one after the other for 1 minute each, you will be doing better than the men attending the exercise class!