Up until a few weeks ago, 2007 was the earliest I’d found Diana Nyad claiming to be the first woman to swim around Manhattan (see The Score, 21 June 2007). I assumed, then, that Nyad waited for her six predecessors to pass away before leapfrogging to the front. The last-living of those six swimmers, Diane Struble, died in 2006.
I apologize to Ms. Nyad for assuming the worst. I was off by over a quarter of a century. Here’s Janet Filips writing about Nyad for the Journal Herald in Dayton, Ohio, on October 31, 1981:

The timeline as it stands now:
1975: Nyad becomes the 7th woman to swim around Manhattan. Or not.¹
1978: Nyad writes about the 1st and 6th women in Other Shores.
1981: Nyad claims to be the first woman around the island.
One other thing: I can’t find those “11 men” Nyad dug up. Using the Marathon Swimmers Federation database, I count six men who made eight total swims before 1975. But if I count both men and women (but not total swims), and if I assume Nyad missed one person, then I get eleven.
Maybe Nyad meant “men” in the sense of “mankind,” then decided it didn’t suit her purposes.
Whatever way she got to eleven, she leaves me with more than two decades unaccounted for, Manhattan-first-wise. I’d be much obliged if anyone can find evidence of Ms. Nyad claiming, at any time(s) between 1981 and 2007, to be the first female hominid to circle the island.

NOTE
- Morty Berger, founder of NYC Swim and organizer of many Manhattan circumnavigations, addressed Nyad’s Manhattan swim in a 2015 email:
[T]here is some controversy if it was assisted or not (My interviews of her boat captain stated she touched/held onto the boat).
As Diana knows, touching or holding onto the boat should result in disqualification and an immediate end to the attempt.