I like your theory. I did see the exchange between Ward and Coulson too, only I thought it was Coulson starting to suspect Ward. There was also the scene where we see Coulson tell Ward something but we don't actually hear it. It was done to lead the audience to believe Coulson was telling Ward that Paxton was a traitor. Maybe he was handing him the gun and telling him what he had to do to gain Paxton's trust and find out more about Hydra.
The only potential "flaw" I see in your theory is if Ward is faking it, then why would Paxton go along with it.
Surely he would know if his former trainee was Hydra or not. No?
P.S. - I like how we all call Paxton by his real name. Does anyone even know his character's name?
Spoiler:
