For cap and ball,other muzzle loaders pure lead is the right thing.
For your Sharps.. You know,you probably are not talking about a lot of metal.
No need to get too carried away overthinking it.
If you do not have lead hardness testing tool,and if you don't know the alloy of the "hard cast" bullets you have,some guesses and assumtions will have to do.
Now,for future reference,Mike Venturino's "Shooting the Buffalo Rifle" And a couple of Paul Matthews books will give you plenty to work with.
A common commercial cast bullet alloy might be 20 to 1,lead to tin.
You might look up Lyman # 1 or #2 alloy,to get some ideas.
What you have is an unknown.
At this point,you don't know what your rifle likes.That matters in the mystery of BPCR.when you go for ultimate accuracy.
But the Olde Buffalo Hunter got by.
Wild guess,30 to 1 might be near what you need,+ or -.
Odds are good,your bullets are about 20 to 1.
So,try 2 lbs bullets to 1 lb lead,load some and see what happens.
Lube matters with BPCR,and the SPG lube is a good choice.
Good Luck!