I don't think they'll make that mistake. The "United way" is a mantra of the club fans, not a billionaire club owner.
Remember they sacked Moyes to go for a proven manager (Van Gaal does have a successful career and actually did well managing the Netherlands). That means the "United way" was thrown down the gutter with Moyes.
They can't afford another failed experiment. MU already has deep problems, which will be aggravated by missing out on the CL this year (they'll find it harder to attract better players and will miss out on CL money). If they keep up that situation for another 2/3 seasons, they'll turn into another Liverpool for the next decade. By then Jose will be at another club.
Also, let's say Giggs turns out to be a decent manager. "Decent" is not enough to compete in a league with Guardiola, Wenger, Klopp, Pochettino and perhaps Simeone. He'd have to be world class. What are the odds of that?
Choosing between Giggs and Mourinho is choosing between the hope to get 4th place or the hope to get 1st. I doubt the owners will think twice.