I know what you mean about being terrified that your kid will cut a finger off, but there are right ways and wrong ways to do things. The fundamental difference between a decent professional cook and a home cook is that the pro has to do it very fast and clean, and this means he or she has to do it right. Now is a very, very good time to start learning to do it right. It sounds like you don't have a lot of terrific skills yourself, so maybe you guys should work on learning some of this together.
Start with steak. Surely you like steak? Get a decent probe thermometer, a heavy pan, and some medium-thick steaks. Now he's ready to go. He should season the steak with salt and pepper as he thinks best, maybe trying a range of quantities. Have him poke the steak with his finger a few times: this is what raw meat feels like. Remember it. Now heat the pan over high heat for a minute or two, dry. Add a dab of high-heat oil and wait a few seconds until it shimmers. Put one steak in the oil, move it a bit as it's going in, and slide it to one side of the pan. Repeat until all the steaks are in. Cook about 2 minutes on that side, then flip the steaks with tongs. Cook 2 minutes. Flip again. Now have him poke the steak. Does it feel raw in the middle? Cook it longer. Consider probing them with the thermometer: what does 110F feel like? What about 120F? Cook until one feels just barely firmer than it was, remove that one to a warm plate, and cover with a dome or a bowl. Keep going like this, feeling how the meat is getting firmer. When all the steaks are under the dome, wait 10 minutes and then serve. Another fun thing: if you cook two steaks exactly the same, try cutting one immediately out of the pan, and the other after 10 minutes under the dome. See how the first one was gray on the outside and bloody on the inside, and the second was a lovely pink throughout? In time, he will be able to tell when meat is done just by poking with a finger.
With luck, if he finds this enjoyable and interesting, he'll have learned a great lesson: cooking well is largely about knowing how to do things, not numbers and timers and recipes. (Baking is different.) With that essential lesson learned, if he still thinks this is fun, he's well on his way.
A note about knives: the bigger and sharper (within reason), the better, provided he knows how to hold the knife with his strong hand and what to do with his off-hand. He can practice this with a butter knife if you prefer, but at some point he's going to have to cut something real. I'll assume he's a righty, OK? Hold the knife in the right hand, gently but firmly pinching the blade between the ball of the thumb and the curled forefinger. The remaining three fingers are curled quite loosely around the handle, rather like holding a pool cue. The left hand forms a claw, with the fingertips and tucked well under. The side of the blade is pressed against the curled backs of the first two fingers of the left hand. You'll notice that he now cannot cut his fingers: the edge of the knife is held away from the fingers by the curled knuckles. As he cuts, the left hand glides leftward along the food, not uncurling and exposing those fingertips. The blade stays pressed gently against those knuckles as a guide. Once this becomes natural, which takes a little while, it becomes very difficult to cut yourself with a knife so long as you pay some attention to what you're doing. But little knives and dull knives are more dangerous: little knives twist too easily, and dull knives require force (and serrated knives are worst!). So a biggish, sharp knife and this basic technique will keep him safe and train him in one of the most essential techniques of the kitchen.
Don't panic. Chefs have been training as apprentices from age 10 for generations.