You're looking for your own boat right? Not sharing with others.
I think you'll find that Toucan, although they have 3 boats, will need them all in the morning. All three went out daily when we were there the 1st week of June. They'll likely suggest you dive with them on both their morning and afternoon trips. btw, one of the afternoon trips it was 2 of us and a Dutch couple. For $18 pp. It's convenient too, either eat there or go across the street to this little sandwich shop while waiting for the PM departure.
Buddy's charters their boats, but maybe not in June - I don't know. I've read Photo Tours Divers at Port Bonaire will charter their boat also. And Menno at Deep Blue View has a RIB(rigid inflatable) that he sometimes takes small groups out on. But that's a rough ride so probably not good for your wife.
Another thing to consider is that there are several really good dives at some of the resorts. The divedocks at Habitat and BD&A have a bench for gearing up on the dock, then 10' down steps to the water. The steps are kind of slippery, they're wood and get soaked regularly. At BD&A they have these stepped down cutouts in the side of the dock, your wife could sit with her feet in the water, you bring her gear to her, then all she'd have to do is push off. So low stress on her back. It's only about 4-5' deep though so inflate the BC or she'll hit bottom.
And BD&A is Bari Reef, which is the best in the Caribbean for fish species. You can even do a REEF fishcount there with/without a naturalist. I think it's about $40-50 for him to accompany you but it's worth it as he points everything out on a u/w slate.
Habitat has two sites off their dock, La Machaca and Cliff to the north. Buddys, Divi, and others have similar dock arrangements - I just can't remember them.