There is no need to connect a kitchen island to the rest of your kitchen. The above design shows how a small kitchen can still have an island. You simply have to make the kitchen island itself smaller and more minimalist.
This style goes well with minimalist stool designs that creep beneath the island itself. Stools do not take much space, but in a small space, every space counts. Choose a stool model that allows for “storage” under the island when you’re not using it.