Will Smith -- Did Not Threaten to Shoot Killer ... Family Lawyer Says

Will Smith did NOT threaten to get his gun and shoot Cardell Hayes before Hayes unloaded on Will and his wife ... this according to Smith's family lawyer.

Attorney Peter Thomson just addressed the media ... and painted Hayes as a bizarre coldblooded killer who not only initiated the conflict ... but cowardly shot Will in the back 6 to 8 times as he walking away.

Here's the version of the story Thomson told, according to Will's wife, passenger and other witnesses.

Will's car was leaving a restaurant when a Hummer stopped suddenly in front of them -- forcing Will to slam on his brakes.

Believing there was no contact made and no damage, Will drove off -- only for the Hummer to give chase and "ram" the back of Will's SUV so hard, he shattered the back windshield.

Will got out and the two men exchanged words ... insisting Hayes was "enraged ... yelling and cursing."

Will's wife and another female passenger got out of the car and tried to diffuse the situation -- and "after some time" they began to walk Will back to the SUV.

That's when, according to Thomson, Hayes followed them and opened fire -- striking Will's wife Raquel twice, once in each leg. She collapses.

"The killer then unloads 6 to 8 shots into Will's back."

Thomson says Hayes then stood over Smith's dead body and began yelling and screaming.

When asked about reports Will had threatened to get his gun and shoot first, Thomson adamantly denied the claims.

"I'm aware of nothing that Will Smith did that would cause this killer to be afraid of his life to the point where he would follow him after the situation would be diffused," Thomson said.