Officially it's a bad idea.

In reality, it's never harmed me.

Wear heavy gloves and clothing, and a welding mask. It's really overkill but safety is always good.

Use a screwdriver you don't care about.

The official way would be a shorting stick (essentially something with some resistance to it).

Sorry I can't offer any insight on discharging your microwave capacitor, but I noticed you intend to scrap/recycle the parts of your old microwave. I recently replaced the magnetron assembly in my microwave and I was wondering how to dispose of the old one. I would prefer to recycle it if possible, but I'm not sure who recycles old microwave parts in my area. Could you let me know how you recycled your microwave parts?

I recently replaced the magnetron assembly in my microwave

And you have the equipment to insure that there is no harmful leakage from the repaired unit - RIGHT?

As far as recycling the magnetron, a scrap yard would be the only option I know of most places. The fact a bunch of our electronic junk winds up overseas should tell you how well we are equipped to deal with it.

Microwave caps have what is called a bleeder resistor in the circut. They discharge themselves. The diode is the one that brings up the voltage. The old magnetron is a piece of junk. Brake the magnet off of it and give it to your kids to play with that is the part that is recycled and throw the rest in the garbage. If for some reason the cap does not discharge and that is almost impossible the discharge will cut your screw driver in half and the cap could explode in flames. This recycling crap is just that. A nice way to say we might think of something to do with it. Untill that happends it is crushed. Only 7 percent of plastic is recyclable and they think 31 percent of metal is recyclable. The rest is contaminated and not useable. The transformer of your microwave is the only thing worth anything but you have to remove all the copper windings from the iron laminates. Shouldn't take more than a few hours. You should get about $12.00 for the copper at todays prices. Good luck.

"...discharge will cut your screw driver in half and the cap could explode in flames."

They are not that powerful.
They can draw a decent arc though so be careful.