I believe @Libranova's answer is brilliant! So I upvoted, and if it's the most helpful, please accept it as the answer.
I'm going to address the issue of throwing.
However he just suddenly begins to throw things as a ‘game’.
It is a game. It's called Getting Mommy's Attention. Sometimes the game is called Getting a (Strong) Reaction out of Mommy. The stronger, the better. It is true that negative attention is better than none, and also true that at this age, they are testing independence, so can be defiant and bossy.
Kids respond well to praise, so if you want a positive reinforcement to not throwing things, one possibility is a sticker chart. For every, say, half hour that he doesn't throw anything, he puts a sticker on his sticker chart. At the end of the day, he can trade a number of stickers for something he likes/wants: an extra bedtime story, a visit from the tickle monster, whatever. But it has to be a decent number of stickers (say, 20). Before starting this, it should all be explained in a way a 4 y.o. can understand, and it needs to be consistent. And the reward needs to be "extra": if he usually gets a visit with the tickle monster, this is a second visit. The parent will know the best rewards, and you're going for behavior control, not sadness, guilt or anger. Not earning enough stickers should be met with a loving response ("I know you want an extra story, and that you're sad that you're not getting one. I'm sad too, because I love you, and I want you to be happy. So maybe tomorrow, I can help you to get more stickers by setting a timer for every half hour? Let's try that.")
You stated you're not a fan of time outs. Lots of people agree with you. But the true purpose of time outs isn't to punish, it's to learn consequences, reflect and gain the ability to control oneself. It's a form of behavioral control, not psychological control. Behavioral control (setting boundaries for behavior) is good for children. Psychological control (using guilt, making a child feel bad about themselves, etc.) is not. One addresses behavior, the other addresses the child's self.
Time outs are a lot of work, and they need to be applied consistently to work. I recommend 1-2-3 Magic by Dr. Phalen. It was given to me by my Pediatrician when I first gave birth (it was a pamphlet back then!) and it's a method I highly recommend. I used it on my kids, and now it's being used on my grandkids.
I still like the idea of things he can throw. :) I hope it solves the issue. If he's throwing for attention or a reaction, however, it might not work. Good luck!
Article about behavioral vs. psychological control (I love Dr. Darling, but then I would... it fits my parenting style, and my kids had chores...)