Would it be safe to mount a metal adapter to my cameras hot shoe or would I risk damaging it by short?

The hot shoes I am familiar with are designed to accept metal cold shoes. You can tell by looking closely at the shoe on the camera, the contacts will be slightly recessed and only have contact when connecting a device that has contacts meant to push into these recesses.

Also, hot shoes should have a protection circuit in them as well. Cameras can get tossed into some nasty situations.

You should be fine.

Maybe. To be absolutely sure not to damage your camera, you can place a piece of self-adhesive plastic tape over the bottom plate of the accesory shoe to prevent any electrical contact between the metal plate and the camera contacts.

If it shorts the front contacts, there may be damage.

Your camera uses the Sony Multi-Interface Shoe (MIS), which has a whole lot more contacts than the hot shoes found on other brands.

One pin in particular brings the full, unregulated battery power, with a 1.6A fuse (Pin 17 in the Wikipedia link above). If this pin is shorted to ground (such as the metal shell of the hot shoe), it would certainly blow the fuse, and anything that needs power from this pin would no longer function. It's not clear if this fuse is self-resetting, replaceable by Sony (likely expensive), or not replaceable at all. Other pins may or may not also have problems, but this one we can be sure about -- it's called out in the spec as an unregulated connection straight to the battery.

Of course, if your metal cold shoe doesn't reach far enough back into the mount to make contact with the pins, then there's no problem. But if I were you I'd double check this very carefully before trying it -- perhaps do a test fit with the camera's battery removed.

Sch*matics of the A*7 exist online, enough said.

Pin 17 is switched from the UNREG_ACC bus via a power MOSFET Q6502 controlled by the IRIS0 pin of the main SOC.

UNREG_ACC is switched by another power MOSFET Q6501 controlled by power controller IC6501 straight off the battery. There is an 1.6 amp fuse F0006 protecting that bus. This fuse does not appear to be self resetting. This fuse does not appear to be replaceable unless you have good SMD soldering skills. There is no evidence of UNREG_ACC powering anything else besides pin 17.

It is likely that a short of Pin 17 while powered would destroy the fuse. It is not likely this would do any further damage to the camera.