Magnificently. That's how he would have handled it. The guy had like 2 losing seasons ever. He had more coaches go through there than Miami Airport.
He built a team around Unitas, another around Csonka, and another around Marino. He found guys who could do stuff and built systems and recruited coaches that could use the stuff they did well.
He regularly drafted low and didn't have the advantage of free agency to plug his holes. He made his team physically superior by working them mercilessly (today they have 17 padded practices and rarely a two-a-day, but Shula had them doing four-a-days without water). He drilled knowledge and discipline into his troops so they were regularly one of the least penalized teams in the league.
He dominated physically, intellectually, and relentlessly. As Bum Phillips said, "He could take his' n and beat your'n, then turn around and take your'n and beat his' n."
Yeah, Don Shula would have succeeded in today's NFL.