There is a tendency to greatly overstate the significance of the bullet diameter of the .38 S&W vs. that of the .38 Special. Most will be unable to see any difference in the grouping performance using the typical .357-.358 .38 Special lead bullet in reloaded .38 S&W ammunition fired in a .38 S&W revolver. For a very long time I used 125 grain .358 lead bullets for loading .38 S&W, and they worked fine. I have seen reloading manuals (I think Speer) which recommend using .357 bullets for .38 S&W reloads. Also note that the minimum SAAMI lead bullet diameter spec for the .38 S&W is .355". If you want to use a .360-.361 bullet, Missouri Bullet Company sells them. But if you have any .38 Special lead bullets you can load, try them first.

I once came across a large number of very old loose .38 S&W cartridges cheaply, and I had a high rate of misfires. I pulled the bullets from the dud rounds to salvage the components, and guess what I found? The bullet diameters measured to be .357-.358.

BTW, I have always loaded .38 S&W using .38 Super dies. It works fine.