Marty,
The best Fred Noonan tree (IMHO) that is public on Ancestry is Jerry Hamilton's.
The very best way to have a reference DNA sample for Noonan is from Noonan himself, in other words something like the saliva behind stamps, assuming they were licked rather than wet with water. As long as the stamps have not been removed, the DNA has been "protected" from contamination and most likely protected from heat, moisture, etc. The need for multiple samples would be to eliminate the possibility that someone else licked the stamps. As long as one sample was from the last flight (and did not belong to AE), a DNA match with any other Noonan sent stamp/envelope would still work.
Having the above DNA as a reference is far better than DNA from a distant relative. Even with ironclad sourcing for the genealogy, there is still a chance for error, even following maternal lines only.
Even so, I have just found someone yesterday, that I believe is a MtDNA match to Noonan. The links between generations need much closer scrutiny, however.
Linda