I don't cast for 9mm or 38 Special, but I do for 45 ACP and 45 Colt. Similar situation because 45 ACP generally is .451" and 45 Colt is .452".
I have tried using round nose 45 ACP cast bullets in the 45 Colt, and the accuracy was very poor. However, SWC 45 Colt bullets were very accurate in the 45 ACP, but there were feeding problems in some of my 1911s, in particular my Dan Wesson Panther, which would not feed them at all, they just stick on the feed ramp (every other bullet feeds flawlessly). They feed fine in my Colt Series 80 and in my Sig Ultra.
So, long story short, it's worth a try, but mileage may vary...
Generally, it is better if the bullets fit the 38 Special groove diameter, they can be one or two thousandths large and still work fine in the 9mm. The .358" die is fine if it actually drops .358" bullets or larger. Dropping at .359" is better. That will depend on the alloy you use. More antimony in the alloy will make drop larger.
