Your gun is a "D" frame gun. All the Colt Detective Special, Cobra, Agent, Police Positive Special, and Diamondback guns are "D" frames.
The SF-VI wasn't made until the very late 90's, and is internaly a totally different gun.
By short grip, I mean the grip is square on the bottom, and is covered on the bottom by the wood, which overlaps the butt. The older full grip is rounded on the bottom and the wood grips are flat panels that leave the edges of the metal grip completely exposed all around.
When you order the grip from Hogue, just give them the serial number, (minus the last two digets) and the year it was bought. They'll know just which model of grip to send.
These older Colt "Dick Specials" are very fine guns, enjoy.