That would have been my advice as well. My best advice to you is to just let any high power laser conversation go for a few months. You've already learned why not to break your "Kid Mad Scientist Security Protocol" by going for up-front full disclosure with your parents. You should NEVER have mentioned burning, ever. You should have just said, "I need 200mW so I can have it show up well for a laser show I want to build out of scrap motors and mirrors." etc.
I totally sympathize. Diode lasers didn't even exist when I was a kid, all I could get were surplus HeNe tubes from American Science & Surplus. Just a few mW, but the high voltage power supplies could certainly be tricky to deal with... And the 1000+ Volts might have made my parents say "No"... had they thought to ask.
And the first diode red pointers that came out when I was a teen were $100 and maybe 2mW at best. Way out of my price range.
However, I still did all sorts of "dangerous" projects and experiments. I figured out that old 1950's chemistry and electricity and science experiment books for kids had stuff no one would dream of having kids do by the 1980's or 1990's. So I built stuff like a carbon arc furnace in a clay flower pot using carbon rods from batteries I cut open, some curtain rod in the basement, a "suicide cord" I cut from an extension cord. A "salt-water-rheostat" from a glass ashtray, some lead fishing sinkers, and bare wire.
Did I go ask, "HEY MOM AND DAD! CAN I GO MAKE A 2000 DEGREE CARBON-ARC FURNACE THAT PLUGS INTO THE WALL AND AN ASHTRAY FULL OF WATER?"
Hell no I didn't.
I just said, "Is it okay if I poke holes in this flower pot to do something from this experiment book?", "I need this ashtray as a dish." "I need to bend up some of these old curtain rods, is that okay?"
When I was done, and had an arc buzzing away like a frigging WWII air-raid searchlight, THEN I called my parents in to see it. They were like "Holy.... ****" but at least were able to decide I had done it successfully, and that I hadn't killed myself or burned down the house.
Am I telling you to LIE? No. I'm telling you to show some discretion in what you say. And to learn that it's easier to beg forgivness than ask permission all the time. This will be something important to understand not just when you're an underage kid, but when you're a grown man with a wife as well. The point is to think ahead about what you do and what you say so you are never asked any questions that you'd need to lie in answer to them.
A fine line? A gray area? For sure. However I'll state flat-out that I think a kid with an interest in electronics, lasers, technology, science and engineering is important enough that a little moral ambiguity to get him some experience is worth it.
You need to take the same approach. I suggest that you get into cheap flashlights from Deal Extreme, electronic parts kits, LED light projects and "safe stuff", like other eye-safe 5mW modules from places like Axiz or Deal Extreme, until you've got a critical mass of electronic project stuff laying around, your own workbench area full of wires and junk and they're used to letting you work with a soldering iron etc.
Then one day, maybe this coming spring, or next summer, go ask to buy a cheap high powered DVD-Write drive so you can harvest some parts for it for one of your projects. Don't go into any details you don't have to. Don't go saying "The DIODE IN THERE WILL BURN! YEAH! CAN I? CAN I? CAN I? PLEASE?" etc. Stick the diode into the 5mW module and it's host that you've already built.
Then go build your 200mW burner.
See how this works?