Tennis, swimming and softgolf ball are all sports that use a lot of arm strength. Tennis, in particular, uses a lot of wrist strength and might be your best bet in improving your swing. You do not have to be a tennis pro to go out there a couple times a week and hit some golf balls. And I guarantee your wrist strength will increase within a few weeks.
In addition to unrelated exercises, drills are always helpful in improving your golf swing.
There are many many drills available online and elsewhere. All you have to do is hop online and search. One example is to focus on following through with your swing, without actually hitting the golf ball. Stand on the golf course with your club, lean back on your back toe, take your club behind you with both hands and swing out in front of you, with the weight shifting to the front foot.
Do fifteen sets of this drill and see how you feel.
There should be a mild burning sensation in your wrists. That means you are doing it correctly. This particular drill should eventually help you improve your swing.