I’m surprised you don’t have a shut off valve at the thru hull before the intake hose goes through the V drive.... I would double check this first. If you absolutely must change it in the water with no shut off I would get one of these:

https://www.harborfreight.com/6-in-long-nose-locking-pliers-63870.html?cid=paid_google%7C*PLA+-+All+Products+-+Lower+Sales+Items%7CNew+Products+-+%281%29+Price+%3C%2410%7C63870&utm_source=google& utm_medium=cpc&mkwid=sNKimAzuo%7Cpcrid%7C318476002 950%7Cpkw%7C%7Cpmt%7C%7Cpdv%7Cm%7Cslid%7C%7Cproduc t%7C63870%7C&pgrid=63088204786&ptaid=aud-454408222021la-297256066520&pcid=1654049980&gclid=CMGuxfe-2-ICFYK3wAodo4AC_A

It’s what I use to pull my impeller every fall..... it’s easy to get it in the hole and clamp it down between 2 vains on the impeller. Then with a little bit of wigglying and pulling at the same time it comes right out..... Much easier than using the puller and faster too...... maybe you could also pull the end of the intake hose off the impeller housing and hold it above the water line.... I would think this would stop the flow of water flowing into the bulge and water won’t be rushing out of the impeller housing while your trying to install the new one.