ESD protection when working inside laptop

I was wondering whether anybody can verify that this set up will work; I want to open up my laptop, but do so with ESD protection. I’m going to use an anti-static wrist strap which I’ll connect to an anti-static mat. I’ll work on top of this mat. As far as grounding the mat goes I’m open to suggestions. Currently I’m thinking of joining the alligator clip from the mat to the metal case of some appliance that’s already grounded. For example I have a toaster with a grounded metal body, that I could attach the alligator clip to and then plug into the wall with the outlet switch turned off. I’m in Australia, and I believe the ground connection will remain connected even if I turn the switch off at the outlet? I was wondering whether 1) this setup will effectively dissipate static charge to ground? and 2) if this seems a reasonable way to set things up with regards to both safety and convenience?