The are probably some on this board that are capable of this task. I am not among them. I would say, it's definitely a job for a gunsmith. A couple of questions come to mind:
Why are you considering a barrel change?
Is the barrel currently on the gun damaged?
Do you already have the barrel you want installed?
The cost of having a Security Six rebarreled may exceed the value of the gun. If the barrel on your gun is not damaged, why not pick up another Security Six in the barrel length you want. You can still find them on the used market. Around my AO a good one can be found in the $200 range. After you pick up a SS in the barrel length you want, you could sell the one you don't like and come out even money wise. I have a 6" Security Six in stainless, it is a great gun! I prefer 4" barrels in revolvers, but wouldn't part with mine. It is a great shooter. The 6" barrel is not a show stopper as I only use it as a range gun. Good luck, and welcome to the board!!
Savage