A very good question. As you said, the personality of the kid matters. Be certain to leave the speaker grilles on your speakers. Bare drivers invite little fingers to poke them.
In general, based on my own experience, I'd say you can begin to trust boys and very inquisitive girls by about 4-years-old. It depends on how well they listen to you and how much they fear the threat of punishment. I know the levels of parental discipline vary widely, so you have to judge for yourself. With my own kids, I learned when they were about 2-years-old that my wife & I could not reason with them about certain life-threatening things. If they ran from the front yard into the street, they had to learn immediately & painfully not to do that. After a few episodes of that, they learned to obey verbal commands. Once you've gotten there, you can tell them to stay away from "daddy's toys" and expect them to follow your wishes.