Jason Garrett was hired by Jerry Jones before Wade Phillips. The odds are extremely high that Jones will not disrupt the established offense by getting rid of the same coach he has the most confidence in. That leaves the defensive side of the ball and Shanahan isn't a defensive coach.
I've said all along if another "name" head coach would be brought in, it would be Bill Cowher. Jones will not relinquish general manager responsibilities and that would be Holmgren's first requirement. The defense is already established and Jones will not take a step back by blowing it completely up for another coach.
On record, Cowher had one main hangup with Jones and that was rectified during last offseason. He would consider coaching in Dallas, but it would be on Jones to make it as enticing a prospect as possible. One requirement for him would be control over establishing the coaching staff. That would be a primary deal maker or deal breaker.