Well, if you don't want to spend the time changing the bettas water, you should look into a larger tank. They are VERY hardy animals, but when they are cold their immune systems are lowered, and then their body can't handle all the ammonia poisoning they get from dirty water! What I'm saying is while he may be happy and active now, he could and will very quickly turn for the worst, there is a reason why most people who buy fish only have them last for a few months... Your fish could live for 3 or 4 more years if you upgrade him! Get him a nice 5 gallon, then you don't have to change the water as much and he'll swim so much more and be crazy! :)
Exercise would be done by giving him more room to swim, like a larger tank(you can buy plastic critter keepers for very cheap), and by letting him flare and swim around!
The net will hurt his tail, it's best to get a 'brine shrimp net' or just use a cup to scoop him out, otherwise his pretty tail can get ripped and torn and get infected(especially if in dirty water!)