Ragnarok, I am a fan of Altamont's as well, I have close to a dozen sets.
I have a set of Super Rosewood Bateleur Altamont grips on my 6" nickel 586-1, I love these grips!
The S&W medallions are nice, but they will fool no one into thinking that they are original.
I have a set of the Altai grips too, I do not think that these are going to work for your square butt 586. These are made for round butt guns to give the grip feel of a square butt.
Here they are on my 686-CS-1
I think that you need to look in the K/L frame square butt section.
Smith & Wesson K/L Frame Square Butt Revolver Grips | Altamont Company
RJM6120 is correct on the ship times from Altamont. If it is in stock, it will ship right away, if they have to make it, two weeks or so. They will send you an email and give you options if it is out of stock. They have always taken less time to make an out of stock item then their initial time estimate.