Well if all you're trying to do is burn off energy, there are better ways of doing that. Bring your kid to a park or indoor play gym, and let him go wild. You can read a book or surf the web while you're there.
But at the risk of reading too much into this, it sounds like your son's hyperactivity may be more than just high energy levels that need to be burned off. I recommend seeing your pediatrician who can then recommend a strategy for tackling this issue. Or maybe you don't know if it's an actual "issue" yet, but your pediatrician will be able to figure that out for you.
If your son is truly hyperactive, he almost certainly won't do well in martial arts classes. Or for that matter, any structured environment. That's because hyperactivity results in a lack of ability to stay interested in and focus on something for any amount of time. Martial arts classes requires the ability to listen to the instructor and stay focused all the time. It's too much to ask of a child that's hyperactive.
I've seen hyperactive kids from the ages of 4 through about 10 in martial arts classes, and it's a terrible thing to watch. They're fidgety. They're not doing what the other kids are doing. They're laughing, sometimes screaming, or talking to themselves while the instructor is trying to get the students to do something. They look like they have no interest in what's going on, but in truth, they just lack the ability to stay calm, focus, and maintain interest.
Almost all martial arts classes that have young children in them will have at least one or two kids like this from what I've seen. And from what I gather, often times the parents of those kids just see the class as an affordable way of babysitting them after school. After school lets out, they get taken by bus or carpool to the martial arts school. And then their parents pick them up after they get done with work. It's cheap after-school daycare. That's our modern life for you.
I feel bad for any instructor who has to deal with it. And I've talked with a few about this before. They just let the hyperactive kids do whatever they want, so long as it's not hurting anyone. It's because they can't control them. They keep trying, though. They say that when they actually get those kids to do something, that's when they feel great. But it doesn't last long.
At age 4, your son is about to begin attending kindergarten classes. That's when this will become a real issue for you. Working him out to burn off energy might help him fall asleep at night, but it's a red herring. It won't help him stay focused in class.
If your kid is in daycare or pre-K classes, you should talk with his teachers to see if his hyperactivity is expected or above what they normally see. They might not be willing to tell you anything bad about him for fear of losing their jobs. So you might want to drop in a couple times to observe his class without him knowing you're there.
Sometimes hyperactivity in children this age is caused by a kind of allergic reaction to certain foods, certain chemicals in food and other products they ingest (toothpaste, for example), and chemicals in the environment. It's tricky knowing what's the actual cause. And your pediatrician might know a specialist who can diagnose this better.
I was a hyperactive child at that age. My mom didn't know what to do, but she ran into someone promoting the Feingold Diet, which eliminates artificial colors, flavors, preservatives, etc. It's since been mostly debunked. But something about it worked really well to prevent my hyperactivity.
When I was about 5 years old, I remember having a hyperactive episode. We were getting ready to attend church, and so my mom told me to go brush my teeth. I went to the kids' bathroom, but the tube of my special toothpaste was empty. So I went into my parents' bathroom to find more toothpaste, and I just used theirs.
Almost immediately, I went crazy. I was running around, screaming, kicking things, turning over chairs and sofas, etc. It was so bad, I remember kicking a hole in the wall. I went from completely calm to completely hyperactive in a matter of minutes. They tried to get me to go to church that day, but we ended up turning the car around and driving back home, instead. I was flipping out in the car.
After about an hour had passed, my energy levels came back down. I calmed down completely. Trying to figure out what went wrong, my mom asked me if I ate anything I shouldn't have just before going to church. I knew what I could and couldn't have, according to the diet my mom placed me on. I said no.
She then asked me to remember the events of the day. And when I got to the part about using the adult toothpaste, my mom said, "Aha!" She ran up to look at her toothpaste, and sure enough, it had artificial colors, flavorings, and artificial sweeteners, all of which were outlawed by the diet. I didn't know that I wasn't supposed to use their toothpaste. Oops.
And just like that, we realized what set me off. It was an reaction of some sort to the chemicals in that toothpaste.
When I was adhering to the "all natural, no added anything, all organic, etc." diet, I was a perfectly nice, calm, normal kid. When I came into contact with any "trigger" foods, I was uncontrollable.
By around age 8 or 9, my body had outgrown this issue. I could eat any food at that point. No special diets were needed. So kids can outgrow this sort of thing.
Anyway, I don't know that this is what your kid has going on. Like I said, the Feingold Diet itself is pretty well debunked. But maybe medical science has some strategies for dealing with childhood hyperactivity, and I'd start by running it by your pediatrician if I were you.
You might want to research it on the web, also. Just beware of all the pseudo-science and alternative medicine nonsense out there. Pass everything by your pediatrician first before acting on anything.
Oh, and as a parent myself, I would be extremely cautious about using Ritalin and other ADHD drugs. I would want to eliminate all of the other possibilities first, and use drugs only as a last resort.
Hope that helps.