Best I could find was a reference (by Darcy Echols) that they used to be made from "spring steel" - in a posting where he shows a "modern" one from a new Winchester 70 that he bent at right angles with his fingers to demonstrate they are not want he wants to work with.
I don't think you can "heat treat" low carbon steel - it is the rearranging the carbon atoms with the iron atoms that creates the hardness and/or spring. And you did actually write "lower carbon steel" as in lower than tool steel, I presume.
Might want to first confirm what kind of 1896 or 1898 mauser the 1600's match up to - until recently, TradeEx had replacement Husqvarna M38 extractors that might have been identical. Maybe there are other mauser milsurp extractors that would work? - seem to be in the $15 to $20 range. Would have to compare, say, an 1894 or 1896 Swede to the 1600 to know for sure - I have the Swede's here, but I only have one 1640 and do not have a 1600 - don't know if a 1640 is same as a 1600.