What type of material is used to shield magnetrons?
I'd think there's actually two different things that could theoretically be dangerous to the computer; leaking microwave radiation, which in sufficient quantities could well induce currents in the metal parts of the computer and maybe fry things, and stray magnetic field from the power source or magnetron, which (as with any magnet) could theoretically do bad things to digital hardware).
Both would be blocked by a Faraday cage--basically a metal box connected to a grounded conductor. In theory, so long as your microwave has a ground pin on the power cable (which I certainly hope it does) the case of the microwave itself should effectively be a Faraday cage.
So far as my very limited understanding of ovens go, that's basically the way the things operate, although maybe they rely more on reflecting the microwaves back in than the grounding.
Meaning, basically, you should be ok (although to be honest, I probably wouldn't do it myself). If you wanted to be paranoid a reasonably-thick piece of metal between the microwave and the laptop connected to your house wiring's ground would be an extra layer of safety.
Would any laptop wires hanging down along the side of the microwave wind up picking up the microwave's EM radiation and conducting it right back into my laptop and external hard drive?
Probably not, but that's the one thing I'd actually be a little worried about (if you had, say, the DC power cord running right along the AC power cord of the microwave).
But then my experience with signal noise on unshielded wires in data collection systems has probably made me unnecessarily paranoid--hard drives are a lot less sensitive to errant magnetic fields than people think.
Note that, while I work with this stuff, it's been so long since my E/M physics classes that I probably have no idea what I'm talking about and am giving awful advice. But then, it's the Internet, right? (And I'm amused at some of the paranoid insanity you get when you search for "block microwave radiation" in Google. Did you know that jet contrails are part of the New World Order's plan to chemically neuter the population?)