Discharging capacitors (and anything else that might hold a charge) isn't that hard and dangerous if you know how. I used to work on radar systems with 32KV on big capacitor banks.

1: Connect a thick, beefy wire to a solid and reliable ground connection.

2: Rig up a way to hold that wire in a well-insulated way, so that you have thick, non-conductive insulation between you and the wire, but you can still move it around freely and easily.

3: Firmly touch the tip of that wire to the contacts of any capacitors you can see, any bare metal contacts you can see, and anything else that might be at all dangerous. If in any doubt at all, touch the wire to it. Do it twice, just to be sure you didn't miss any. (There may possibly be sparks when you do this. That's okay -- it means it's working. Do make sure you're not close to anything that's very flammable, though.)

After doing that, everything will be discharged and completely safe to work on.

For something the size of a microwave, you could build a capacitor discharge tool very simply and easily by taking any three-pronged power cord, cutting it in the middle, disconnecting and isolating the two power connections (leaving only the ground connection), leaving a bit of bare wire from the ground wire exposed at the end, and then wrapping your handle area in some extra layers of electrical tape (just in case some of those capacitors have voltages above ~300V). (Or if you want to be ultra-safe, tape a plastic or wooden handle to the wire instead.) Plug that modified 3-prong cable into any standard 3-prong household outlet to connect it to a reliable ground.

If you want to be a bit more professional about it, a grounding wire from an ordinary welder setup should be able to safely discharge just about anything you'd ever encounter.