Well, the majority of the Aegean islands are in greek hands since the mainland hasnt fallen. I say most because in the OTL the OKW had a specifi interest to Lemnos as it can be developed in a major airbase and controls the entrance to the Dardanelles. Originally, it was thought that a regiment of paratroopers would be dropped there. A Greek retired general did a thesis on those plans a few years back and I have a map with the planned drop zones. Another battalion was to be lifted to Lemnos with fishing boats from Porto Lagos in the thracian coast. I guess the Germans have also occupied Thasos and Samothrace. However, i dont think they will have been able to capture other islands since they can go only so far south with fishing boats before warships make mincemeat out of them. In the original Marita plans they didn't have other island targets after all.In the east, Rhodes is too big to leave. I wonder how many Dodecanese and Aegean islands are the same, and how many can be left to wither on the vine.
The Dodecanese are completely cut off by the Cyclades, Chios and Lesbos. The Germans don't have warships in the Aegean. At best they can transport and assemble some E-boats and small subchasers with rail. The Allies even enjoy the port of Syros as a base. There is a small shipyard there that in OTL was able to service destroyers.
I am under the impression that Churchill would want to recapture Lemnos. As it stands now, Lemnos is more important that Rhodes, as it controls the Dardanelles. Moreover, Churchill knew the island as he had visited the Entente logistics base there in 1915. In April 1941 a british battalion had landed there and RAF officers started surveying the island in order to develop airfields. The battalion was able to evacuate the island well before the Germans captured it.