I was on Orkney recently, and bagged all but one of the 64 trigs. Only Muckle Green Holm got away. I've put some details on the TUK trig page which might help - I'm sure it's doable with a bit more planning than I did (i.e. none).

Here's what I did, in case it helps anyone:

Thu 27 May: a.m. ferry from Gills Bay
Fri 28: a.m. North Ronaldsay*; p.m. Shapinsay; Kirkwall
Sat 29: Gairsay; Orkney Mainland
Sun 30: a.m. Eday**; p.m. Stronsay, Stronsay overnight
Mon 31: back to Kirkwall; Sanday; Kirkwall
Tue 1 June: Wyre, Rousay, Egilsay; Tingwall
Wed 2: Westray; Papa Westray; Kirkwall
Thu 3: Hoy, Flotta, Hoy overnight
Fri 4: Orkney mainland, ferry to Gills Bay, Scottish mainland

* North Ronaldsay sailings vary - was very early morning that day
** using Sunday Excursions timetable - different each Sunday

That was the only way I could find of combining them all in the time available.

I daresay many would take longer per island, but you have to get what you can when you can I loved the trip - nice spring weather and evenings which go on forever. Photos.