Microwaves do not use "radiation" in the usual sense of the word - they use high-energy/high-frequency radio energy. The effect from a microwave is the same as standing too close to a high-powered transmission antenna - the molecules in your tissues (especially water!) are excited and vibrate faster to heat up. This heat WILL cook you from the inside out - there are rarely first- and second-degree RF burns. First- and second-degree burns are primarily surface involved, and by the time it looks like you have one it is already too late - underlying tissue has been destroyed. However, it is useful to know that once the Magnetron has been disconnected, you are essentially safe from RF energy.
There are also high-power caps in the box, DO NOT TOUCH THEM! Simply grounding them to discharge them is likely to result in destruction of SOMETHING, as you have just effectively shorted the cap to ground. You will need something similar to a radioman's "dummy load" to discharge a cap safely.
Put simply, it is possible to service a microwave, but it is also cost prohibitive to do so. The amount of equipment you will need to ensure your safety will cost about three times what a new nuker will go for, and it just ain't worth it for someone who won't have other uses for the equipment. Private individuals who service microwaves are usually radiomen - who have a full understaning of the risks and principles involved...
FFZ