Homotopy equivalence of what? This isnt really a topological space. It is a pair of spaces, one of which is contained in the other, (the sphere and the borders). This changes the category, morphisms are now pairs of morphisms and must preserve inclusion.
The answer is neither, since there is no continuous map that increases the number of connected components of a space and there are more islands than show up on the map.
There are other obstacles as well, alaska adds a piece to canada's boundary, this changes the fundamental group of the subspace, which is an invariant of homotopy type, and so the reduced version cannot be homotopy equivalent to the subspace with alaska's boundary included.
The answer is neither, since there is no continuous map that increases the number of connected components of a space and there are more islands than show up on the map.
There are other obstacles as well, alaska adds a piece to canada's boundary, this changes the fundamental group of the subspace, which is an invariant of homotopy type, and so the reduced version cannot be homotopy equivalent to the subspace with alaska's boundary included.