In working on computers, or for that matter of fact most electrical equipment, avoiding static damage is achieved by establishing a ground plane.
It's not whether you're connected to earth potential, but rather the fact that everything you're working on is at equal potential.
You can get by easily by having an antistatic mat on a desktop that you've laid all the components on, and then grounding yourself to that mat with your personal grounding wrist strap. This establishes a ground plane of equal potential as everything on the mat will bleed charge to equal potential. No potential differential, no sparks...
The same can be done with an unplugged computer simply by attaching yourself to the metal case with a grounding wrist strap and laying the plastic component packaging (antistatic conductive plastic) on bare metal in the case before opening. Once again, you're attempting zero potential between you, the computer case and the component, not absolute earth potential.
As to worries about computer power, the maximum voltage you'll encounter is 24V if you manage to bridge the powered output between +12V and -12V. The line current is pretty effectively contained inside the metal box the PSU resides in except for ancient AT style PSUs with the hot switch that switched full line power. Those could be dangerous.
I've also had situations where there were bad grounds in the power wiring that allowed for hot chassis, so if it's unplugged, you will find this is the safest mode of operation.
If you feel it's absolutely necessary to work on an earth potential chassis, there are green-cords available. They have only the ground lug attached. Using the ground plane methods described, I've never really needed such a thing and I've worked in some industrial situations where there's been some pretty heavy inductive magnetic fields available that have powered up the outer shields of ungrounded coax ethernet cabling. Computer system completely disconnected from all external devices with grounding strap worked the best.