Cayman Brac seems closest to what you want, but still nothing like Bonaire or Curacao.
Cayman has a few good shore dive facilities, but IMO mostly good for supplementing boat dives there not the whole deal. And traffic between them can be a nightmare.
I love Little Cayman but I prefer boat diving. It may be possible to do some shore diving there, but not so practical for a visitor. For starters, unlike Brac not sure there is anywhere to rent tanks.
I don’t think any op will refuse to let you set up your own gear. (Most people do bring their own gear.) Just don’t cop an attitude. Going with most of the flow of a valet op may be easier for both parties though, just watch and check your gear after. When we last dove with divetech (many years ago) they seemed less inclined to do the valet thing, but I don’t know now.