I doubt an air drill would work under water. The exhaust would be restricted by the water, which might keep it from working and could be dangerous. The amount of bubbles generated by the drill would keep you from seeing anything. Oil would be introduced into the pool as well.
Lowering the water level is your best option. You might investigate if a nearby fire department has a portable tank you could pump the water into temporarily. There are large canvas tanks that are used for temporary water storage in areas where there is not much water available.
My recommendation is to use left-handed drill bits instead of an extractor. You have to drill anyway, and the left-hand bit will usually pull the screw out during the drilling process.
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