You're right, Hicks doesn't come across as the kind of person who'd kill someone in cold blood.
However, this is following roughly two-thirds of his squad getting killed. These were people Hicks had likely served with for years. They were his brothers and sisters. He had a solid reason to be more than upset with Burke for this mission being a f**k-up. It wouldn't be cold blood (in Hicks's mind), but vengeance for his Marines.
Yeah, I think Hicks would've gone through with it. It looked as though he was going to lift Burke up, shove him against the wall, punch him in the jaw, and deliver an execution that could easily be covered up. The place was going to blow to Kingdom Come, so it's not like anyone would be able to find Burke's body and suggest he was murdered.
Also, it would be worse if Burke had been left alone with Vasquez. She wouldn't hesitate to grease him if given the opportunity.