Should I remove the plate behind the black mixer cup?

The top screw (encircled in blue) is stripped. Before I go in there with drill bits and screw extractors and ATTEMPT to remvoe the broken off screw, I was wondering if I could easily remove the black mixer cup and the plate behind it (encircled in red). Removing this plate would give me better access to the screw. And if in fact, the plate can be easily removed by unscrewing the two large screws, do I need to shut the water off prior to doing this? I am just a home owner DIY'ing, with limited plumbing knowledge, so any pointers would help. Thanks! Note: The screw was stripped by the previous home owner

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