I think there are a few questions here to make sure we're not giving you unqualified medical advice and that we offer as much help as we can without crossing any boundaries.
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First, how long ago did you break your wrists, how long was your recovery, and how long have you been active/doing your current workout since? Were you given any specific medical advice to follow upon release from the doc?
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How much medical interaction did you have during recovery, and just as importantly, do you currently or are you able to go see a medical specialist for your specific concerns in regards to your chart? Whether asking for ideas on workouts you can do safely with your current wrist situation, or just going over any suggestions that you might get from here to see if they recommend or condemn any of them, it would be worth it to check with a specialist. Depending on where you are the process is different, but if it's a referral system then your primary care physician may recommend an osteopathic specialist, orthopedic specialist, nueromusculoskelatal specialist, physical therapist, pain medicine specialist, etc., whoever the appropriate qualified personnel is to make sure you stay safe instead of getting injured again and make things worse instead of better!
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How many pushups are you currently doing before the pain sets in and before you completely crumble? Do you feel comfortable sharing your current height and weight estimate? Have you tried any other exercises that place strain on the wrists that also cause abnormal pain or the inability to complete a rep, and if so what? And do you have past experience with traditional workouts or are you just getting into it?
The Warm Up/Cool Down is the first step in Flexibility:
Regardless of any of your answers, a big thing is the warm up and cool down. Get the blood flowing and shake it out a bit at the start -- you probably have seen UFC fighters and boxers shaking their arms out and bouncing around before a match, or divers and swimmers shaking it out and doing some neck rotations before getting in the pool. It helps to keep you from pulling something in a bad when you warm up a bit instead of stretching a completely cold body.
Next, ballistic and dynamic stretching are key. The idea of static stretching before a workout is pretty much gone everywhere. It's been shown to wear out muscles a bit and even tighten them instead of loosening them up to the point where it hinders your workout and risks injury. Stick to the ballistic/dynamic stretching before the workout (you can look up good routines or ask for suggestions here specifically).
Afterward, don't skip the cool down, which is just as important! You included a cobra stretch at the end of your routine, so chances are you're already doing this which is great! In general, don't dead stop and walk away from the mat or toss your board (or skates) in your car; walk a bit, do some light kicks and some ballistic stretching, get your heart rate down before the big stretches. When your heart calms a bit is the time when you should definitely do static stretching -- again, you listed cobra stretch so you might already do this step in full. If not, add in more, take care of your arms and calves and all the other areas that need to be stretched out.
This will help stretch your muscles to add some flexibility, but also help stretch things to get the most out of your workout and recovery, from allowing bigger range of motion and helping your small stabilizer muscles build during, and putting your muscles in the best place to recover and rebuild after.
Extra Flexibility: I strongly recommend something that focuses on this at least one day a week. Maybe it's as simple as a bunch of stretches on an active recovery rest day. I myself absolutely need one day of yoga a week or my body ends up in so much pain that I'm walking around like a wooden plank and not able to workout as well. It can be an hour-long tough yoga that causes a heavy sweat, or a really short half hour routine that focuses on simple stretches and calming your nervous system. I always recommend the tough stuff or something in between, but anything is better than nothing. The tough stuff is great because it builds flexibility and helps the accumulating overall body pain from weeks of working out from taking over, but just as importantly it does a ton for balance posture and some stabilizer muscles. This strong balance building, etc., goes a long way in strength training and athletics where proper stance and not falling over during sets really helps you get the most from exercise. And it doesn't have to be yoga, but find something that works for you! Try some things and see what you like best.
Important Disclaimer! While these questions need to be answered to provide more specifics, don't give a ton of personally identifiable information! You don't want to dox yourself accidentally. You don't need to say "here are the names of the doctors I've seen" or "my previous exercise experience is doing varsity tennis at [specific high school name] in 2008" or anything like that. We want answers to be able to give your proper suggestions, not answers that let spammers and scammers come into your inbox, etc.!
Edit: I forgot to ask how serious the injuries were. Are we talking hairline fracture or full on shattered-in-bed-and-casts situation?