I try to give my favored trees at least three sides with room for the crown to expand. Cutting extra competing trees gives more room to expand but exposes the favored tree to more wind. Blow overs are a big deal here.
With ash values being fairly high at this time for good ash, another question is how should you release the oak trees?
Should the ash be cut by loggers and sold, girdled or hinged or simply dropped and left. Skidders damaging roots of saved trees and possibly scarring up trees is always a risk when selective cutting. Skidding only on frozen ground would certainly be a consideration for me as would opting for smaller skidders and not hauling out several whole trees at once. It is pretty much a given though that the ash trees will die on their own soon and maybe no action related to removing Ash trees might be the best action for your oak trees. I'd be surprised if the ash are not already showing signs of weakening-ie, shrinking crowns, less leaves and peeling bark or bird peck holes.