I'm not sure what a "War-Hawk" actually is but I'm guessing it's not a good thing. Most people who are expert at waging war hate waging war. It's what makes them expert and rational as opposed to flippant and hollow. Men and women who are expert at waging war don't issue ultimatums and/or red lines they have no intention of defending. Men and women who are expert at waging war don't issue "junior varsity" comments about an opponent that makes only the issuer of the comment look weak and juvenile.
There are no military men or women running for the Presidential nomination of either party, that I'm aware of. But such a person would be a great option for the times we live in. In the absence of such a leader, I would hope that whomever wins the Presidency next time around will listen to and consult with their military leaders when it comes to these issues and doesn't consult only with political hacks who kiss his/her ass for a living.