This is what I do against every Hawkeye:
Play Sentinel like Zangief meaning be very patient with your actions. In your situation where snapping in Hawk would not be feasible it’s best to try and plink dash in on him with a good assist to hold him down like, say maybe Plasma Beam, Missiles, Vajra, or even your own Hawk assist.
Remember Sentinel is big body for a reason and his boots do help him out a lot in Sent/Hawk match up. He can’t touch you if he can’t get to you and if you place your buttons well enough to the point where he either;
A) Raw tags in to a character more suited for the match up. In this case you should have nothing to worry about since you should have an assist, plus drones to cover the incoming character, or
B) In anchor battles, Hawkeye will start doing random Gimlets wasting bar trying to kill you. More often than not, your Sent will have 45-50% hp left, which means you have to be more careful to block oncoming Gimlet attack. Also, don’t forget that you have kara cancelling abilities into several moves. More specifically his command grab.
In any case just be sure you know how to play your Sentinel well or else he will end up being scrap metal.