Chilled Shot= 2.00% (Antimony), 0.625% (Arsenic), 97.4% (Lead) Brinell 10
Magnum Shot (6 or 9) 4.00% (Antimony), 1.25% (Arsenic), 94.8% (Lead) Brinell 13
Magnum Shot (7 - 8.5) 6.00% (Antimony), 1.25% (Arsenic), 92.8% (Lead) Brinell 13
The above represents some known brands of shot and the contents of their alloy. While they look close, the amounts of arsenic to antimony will add to the amount of hardness you can achieve by using one over the other.
As mentioned usually folks use the shot to stiffen up something like plumbers or pure lead to get something like clip on wheel weight as a final alloy. If as you mentioned this a box filled with mixed shot, I would simply smelt all of it into small ingots, and add it to pure as needed to get something in the hardness range I needed for the 9mm and 357.
If your not running your loads into the 1200fps range with either of those it would only take about an equal amount of the shot alloy to bring up some pure lead into a good range for either of those, and even less for the 38 SPL. That's if you don't water drop them, if you do that you could probably get away with a little less of the shot as the arsenic and antimony will harden up real good when quenched.
Here are a couple of links you should look into,
Cast Bullet Alloy/URL]
[URL="http://www.lasc.us/HeatTreat.htm"]Heat Treating