It is well known that (concerning GMs only) Lilienthal set a record - he missed the 100 only by 3 days. Averbach is very close to beating him.
What about WGMs? It is trivial to look into the FIDE rating list, but e.g. it lists Edith Keller-Herrmann who died 10 years ago. Also, see above, the current oldest living WGM might not be the global record holder. (It might be, since the GM title was introduced only 1950, but remember also "retroactive" titles were given - Keller-Hermann got hers in 1978.)
My guess would be Květa Eretová (assuming the FIDE list includes all deceased GMs too, but at least this is not the case for male GM, as it seems).