From what I'm reading, it doesn't matter what kind of sawdust or shavings you use. Is that correct?
Pretty much. It has to be DRY, you don't want to risk adding wet sawdust or shavings and getting a visit from the tinsel fairies.
I stick with sawdust from poplar/pine/oak/cherry (but those are the woods I cut the most). Sticking with the lighter-colored woods makes it easier for me to see if I'm getting woods that I know will mess up my sinuses. But they all work.
YMMV, of course.
The dry part is VERY important!! The tinsel fairy comes with heat you don't want on your person. The wood chips from my planer are free (sort of- I did pay for the wood it comes from.) and they don't have to by thrown away. I also use them in my bee smoker for tending to my bees. Again, good luck in your casting adventures.
P.S If your cast for those other unmentionable type rifles/pistols, One part 50/50 solder added to 9 parts wheel weight lead (clip-on type) will give you a melt very close to Lyman #2 alloy which is the unofficial standard for those unmentionable types.
doggoner