I am not terribly well versed in NES assembly, and as I tend to come from later systems I find some of its limitations and underlying concepts a bit strange* but it is nothing too troubling. https://wiki.nesdev.com/w/index.php/6502_instructions
*from a PC and GBA/DS where there are dozens of general purpose registers and instructions act like said registers are just part of the command to the NES where there are 3 or so depending upon how you want to view it and instructions are considered as unique to those registers...
Similarly such things are a bit limited compared to later systems with regards to the operations available. Still can do things but you have to build up to it. Some also come to enjoy its simplicity, can't say I do myself but I can see where such people are coming from.
As far as this hack is concerned it should be no great issue as it is not like you are trying to wedge in a whole new routine as much as disable something a game does, tweak within existing parameters or divert existing functionality away from an outcome.
Looking at https://strategywiki.org/wiki/Castlevania_III:_Dracula's_Curse/Items
it seems like this might be a slightly more complex than I thought it might be (I was thinking three drops rather than between 7 and 15 depending upon how it is counted -- the NES being 8 bit means that while you could do random, or a biased random which usually means a different range, between 0 and 15 I could also see one bit per drop type and the sub weapons being kicked to another, which might also help with the different characters being denied different things. Still you should see a random calculation somewhere in there for it all and you would have to figure out what means what there. Or at least enough to tell it "if sub weapon do this instead".
I also had a look at http://datacrystal.romhacking.net/wiki/Castlevania_III
to see if it might have something. Sadly not, and while some of the hacks messed with item stats they did not necessarily have an easy path to drops. Did tell you where the score was held in RAM though so you can start with that if you like for the search rather than find health. Health might be better as things flow from that, as opposed to score which is probably one of the results of it, but easy enough to carry on working backwards for one or two steps.