NavList:

You can determine Zn a thousand different ways. Of course, that's what you do every time you work up a sextant sight. Find yourself any tool that does sight reduction calculations. Easy! Certainly the one that you should be most familiar with is the USNO web app: http://aa.usno.navy.mil/data/docs/celnavtable.php. Enter your lat/lon, date, and time, and it returns the Hc and Zn of visible objects. You could also use many other software tools, like Stellarium and an almost endless variety of smartphone and tablet apps. Yes, you can do it with paper calculations, but that's just Luddite behavior if you're merely trying to decide whether you can take sights from some convenient location. 

As for dip short, if the distance to the horizon is less than the distance to the beach of your nearby island, that means that the beach of that nearby island is beyond the horizon, and you can't see it. You may still see part of the island peeking above the horizon, but if the sea horizon is closer than the island, then you have a true horizon in front of you, just fine for celestial sights. Ignore the visible portion of the island sticking up from beyond. In "short", when the distance to the sea horizon is less than the distance to the island, it's just plain dip --no dip short needed.

Frank Reed
Conanicut Island USA