I did not see a Fast Shot over at the Fallout Vault.
However I use the Rapid Reload and Quick Draw perks and they have no effect on Spread. As they should not as the perk applies to the parts of the action that do not involve shooting.
What will speed up your shooting is Agility. High Agility results in dramatically increased shooting speed
There is a thread from a few days ago where someone did some testing on the Agility and how it effects guns.
EDIT Here it is
http://www.gamesas.com/index.php?/topic/1131013-agilitys-hidden-stat/