Unless I didnt understand this correctly, I think you are risking it. A future job may or may not happen in a timely manner. Why would you use 4-day work week when you have just started a new job? Why would you make up an excuse to claim the 4-day work week benefit. If there is a back story to this, then pardon me otherwise make sure you dont drop the ball with current employer.
Otherwise, many people use after work hours and weekends to prepare for interviews. Take an odd holiday , pull a sicky here and there. This is totally doable. There are tons of thread in the Q&A forum on preparation advice, so please search broadly.
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