Try this website for your search.
https://www.wiewaswie.nl/personen-zoeken/If your grandmother was registered at any time in St. Maarten (or the Dutch Kingdom) then you might have success.
You will want to search for the names you listed in many different ways. For example Katherine Arrindell could be spelled:
Katherine or Catherine
Arindell or Arndell or Arnell or Arrindell or Arrindall or Arrindel or Arrundell
You get the idea.
I have been doing research and I am a descendant of the Arrindell's in Zorg en Rust, Dutch Quarter (or Prinsen Kwartier) The spelling of especially the surname is all over the place.
You will get creative ideas for the spelling the more you use the site. You will want to revisit the site again and again until you find something that can help you in your quest.