I do not agree that there has to be a punishment. I suggest that he be disciplined. The purpose of discipline is to teach. If he's learned his lesson then what has happened is enough. Remember that a 6 year old's brain is still immature. Impulsive behavior is normal. So is experimenting. He wants to know what this can does to a door. He starts and it's fun. He is not thinking about whether or not its right or wrong. One lesson that you want to help him learn is to think before he acts. Another may be to not snoop or be in places which are not the usual places for him to be and to not do handle anything that does not belong to him or which he's not been allowed to play with before. Those are just a few of the lessons. You can't teach them all at once tho you can touch on all of them by talking with him in a respectful manner. Not by lecturing or preaching. Treating him as a kid who made a mistake and can learn from it. Recognize that he will be learning these lessons over time. You are putting information into a brain that is immature whose ability to comprehend totally all of those lessons at one time is limited. And his ability to focus is also limited. So make this discussion short. Perhaps 10-20 minutes. Including his telling you what he heard.
I suggest that you choose one lesson and reinforce that one if he appears to have not learned from your talk. How do you know if he learned. Ask him what he learned and listen. Perhaps clarify for him some part of what you said that he didn't hear.
If you think he didn't understand or you want to further reinforce a lesson choose a discipline related to what he did. For example, let him help repaint the door or doing a chore for the person who is painting the door so that the person doing the painting doesn't have to do the chore.
I don't think this situation is appropriate for grounding or losing privileges unless they are related to the door. An example of a natural consequence would be that he has to stay in the same room with you when you visit the aunt because you can't trust that he won't get into something that is not his.
For discipline to be effective it has to be related to the lesson you want him to learn. If the discipline is arbitrary he learns that he will be punished. Fear is effective for stopping behavior only for a limited amount of time.
I think that having to tell his aunt what he's done and apologize is a good form of discipline. Doing this was not easy for him to do. Now he knows that if he does something that damages someone else's property he will have to tell them and apologize. You can repeat that discipline again when he breaks something or does some other act that damages someone else's property. He's six. This sort of thing will happen again. Lessons repeated are well learned.
While if he gets grounded or loses a privilege, unrelated to the door, he learns to not get caught. You want to teach him a positive way to make what he did right.
We do have to have rules and boundaries with children. I think that sometimes we rush to punish and lose sight of the focus to teach. If I'd spray painted a door when I was his age, I certainly would not spray paint anything else because of everyone's reaction and the trouble I'd caused. My mother would have talked with me about what I'd done, what was appropriate to do in response and then asked me if I understood. My father would have spanked me. I credit my mother for my understanding of the difference between right and wrong.
I was angry with my father until he was an old man confined to bed. I was able to let go of my anger, in small part, because he was now helpless and understood how helpless I still felt when as an adult he lectured me on how wrong I was instead of talking with me about what had happened and how I could make it right.
Later: I agree with Carla S. whole heartedly until the last sentence. "You have to make it suck......" NO! You have to help him feel good about being a responsible boy! Praise his work! I don't know that a 6 yo can mow the lawn but I agree that working it off in the way she described it is an excellent idea.