Cone is a pretty smart guy but I'm not so sold on his potential decision making. Also the stories that would come out about the partying he did in his Mets days once he became a serious candidate would presumably be intense, which is why I think he will never be a serious candidate for NY manager. If he did ever get hired, though, he might be the guy to get them to dump the no beard rule at long last...
From what I know, the move should be fire Boone, promote bench coach Carlos Mendoza to interim manager, maybe hire Beltran for bench coach, Joe Espada (HOU's bench coach who was with NY previously) as a managerial candidate after HOU's season is done (unless they fire Dusty and promote him to keep him, pretty unlikely). I said it before Boone was hired, if it was me picking, I would almost certainly pick someone who spoke both English and Spanish fluently, there are a few options.
Also Boone could then go (hopefully) do something where he would be an actual upgrade, replacing A-Rod on Sunday Night Baseball. Boone was not good either when he did that but much much better than our centaur friend. I know none of this will actually happen (at least until the offseason with Boone) but a man can dream.