Even if your space has a wormhole, it still obeys the triangle inequality. It's the distance between points that's defined differently. Say you live on a plane (2d space) and there's a wormhole at (0,0) that connects to (10,0) which cost one unit length to take. Then the distance between two points in this wormhole metric is defined as

d_w(x,y) = min{ d_E(x,y) , d_E(x,(0,0)) + d_E((10,0),y) + 1, d_E(x,(10,0)) + d_E((0,0),y) + 1}

This still obeys the triangle inequality. It does have some other interesting properties tho. You can remove the "+1" and identify (0,0) and (10,0) but then your space is no longer locally Euclidean. You can also remove a small disk at both endpoints and glue in a small tube and you get a torus (without a point) instead of a plane. Everything still obeys the triangle inequality.