Shoot it with 357 ammo until you are used to it and have the sights the way you like them. I have seen so many people shoot a lot of 38 ammo in their 357. Then when they want to shoot 357 ammo they can't hit anything. This is my opinion on shooting 38 ammo in a 357. 38 ammo is great for introducing new shooters to a revolver. Personally I have a 9mm to plink with something light caliber. When I shoot a 357 I want to shoot a 357.
I have a two Blackhawks I really like. Both shoot federal 158 gr JSP very well. My 6.5" Blackhawk shoots CorBon 200 gr cast bullets the best. The CorBons do not make a big difference 4.5" Blackhawk. It could be the 6.5" provides a much better sight plane.