Not a good idea
If you load a powder charge intended for a .357 Magnum into a .38 Spl. case, that case has less surface area than the .357, resulting in much higher pressures. If those loads got mixed up with regular .38 Spl, or for whatever reason those rounds wind up in a third party's hands, they would probably cause a kaboom. In fact, these rounds could even be hazardous to shoot in a .357 Magnum revolver. On three separate occasions I received a quantity of free ammunition from the wives of recently deceased friends.
When federal law enforcement agencies still used wheel guns, they had developed what was often called the Treasury load which was a 110 grain JHP .38 Spl round loaded to low end .357 Magnum performance. These rounds roared but they were developed by a major ammunition manufacturer (Winchester) with sophisticated measuring and testing procedures to insure they were safe to fire in .38 Specials. Even then, firing them in a 5-shot Chief Special gave one the feeling that the gun would explode on the very next round.