What would be the tactical setup?
Tactically, adaptability and in-match flexibility are the hallmarks of a possessive and progressive style of football. There are similarities with Cooper's in-match formations, but with an added gusto and focus on just taking shots. This is less patient football, but still possessive. There is also a more defensive element to his teams.
Typically, on defence, a Nistelrooy team with mirror something out of Nuno Espírito Santo's books. A compact, high-pressure, low-block with little space in the centre and a sacrifice of the wings. Again, Steve Cooper's team ought to be doing this, but due to a variety of factors this is clearly not happening. This is not always possible with weaker centre-backs and overly aggressive fullbacks.
Broadly, this means a 4-2-3-1 with a proactive goalkeeper supporting build-up plays. In possession, this usually moulds into a back-three with one fullback joining strong central defenders, and one marauding forward to support progression. This is identical to how Cooper supposedly deploys the King Power's starting XI. The difference is that 'RVN' adapts the exact formations and players based on the strength of the opposition: so a 4-4-2 might end up being employed if necessary: Cooper barely changes tactics.
You could expect a senior starting XI of Mads Hermansen, James Justin, Jannik Vestergaard, Caleb Okoli, Ricardo Pereira, Harry Winks, Boubakary Soumare, Facundo Buonanotte, Stephy Mavididi, Jamie Vardy, and Abdul Fatawu. We would also likely see a lot more of Kasey McAteer, and less of Bobby De-Cordova Reid who would - alongside Conor Coady - be the experienced members helping to develop the younger talents.
Ruud Van Nistelrooy would be a massive step up from Steve Cooper, offering a significantly different approach to people and a more adaptable alteration of the same tactical approach. That could rejuvenate and energise an otherwise passionate list of Leicester City players. With the right coach and motivation, the Foxes can survive.