One thing Hawke could do is provide Bucky and Kaine with plenty of distractions to accomplish their own goals. Hawke can be subtle when he wants but he's very good at drawing attention.

I can see him joining with Jaitet and rallying the people together while putting most of the president's attention on him at the same time. This way Bucky and Kaine can move about mostly unseen while letting the guard and the president gun for Hawke. Maybe even get Ke Divan or Mische to help him as well.

That's just one option though.