Distance between features without crossing other features?

[ScottBingo]

I am trying to figure out how to find the distance between features of various types and I have the same issue for each.  I am looking at features along the coastline of an island and would like to be able to find the distance to nearest ocean features, but I cannot have the distance measure crossing land to do so.

For example:  I have a polygon that is representative of a depth layer.  I have points along the coast line.  I want to find the closest distance from a each point to the polygon without crossing land.  In some instances the measurement would cross the island to go to the depth on the opposite side, and, if this is indeed the closest area, I need it to skirt the polygon that is the island.

I also have points in the water that are indicative of certain features which I need to find the closest distance to shoreline points without crossing land in the same way.

I have separate shape files for all features, points, and the island coastline.

Thank you.

Edit: an image has been added for reference.  I am trying to find, among other things, the closest distance between the black points on the coastlines and the red polygon (shipping data), the blue polygon (depth contour), and the yellow points without crossing the islands in the center to measure said distances.

[XanderBakker]

Indeed, as Dan already mentioned, you basically describe the process already suggested by Dan.

However, even if you define the area which is not navigable, your result will not be the same as the image you provided. There are probably more factors that influence the actual route a ship will take: 

You can sum the cost distances from start to end and from end to end to get something like a range or zone that is most likely to contain the route:

In this case I varied the cost based on distance from the cost to get a little more variation...