How to capture unoccupied enemy-controlled territories?
On an island, there wouldn't be an opportunity for a tank blitz (unless it started from a land zone two zones away).

But tanks or infantry can assault an island (or any coastal region) from a transport, possibly with air or battleship support. If they "outlast" the enemy defenders, the survivors can move ashore and occupy the island. 

Tanks or infantry attacking an unoccupied island have "outlasted" the enemy defenders, by definition.