The static risk is small and easy to avoid. Use a wooden or glass table instead of metal and briefly ground yourself each time before you touch the chassis or parts. A wrist strap never hurts.
The far greater concern is snapping or otherwise damaging one of the 4 screen connectors. Watch several YouTube videos before attempting this. Each connector detaches a little differently. A broken connector is so expensive to fix that the machine is essentially worthless.
I recommend a smart phone camera for its LED light source and magnification/zoom A helper to elevate the LCD screen while you work on connectors is the best approach.