Pro's : You will carry.
You can 2v1 3v1 amazingly without a problem.
You nuke like crazy.
You can solo baron.

Con's:
You are the priority
Not that much farm mid game.
Takes a bit for all the items.
People will hate you.
Cant always escape.
Starting top will be rough till mid game.

(start off)Regrowth pendant: Instead of starting off with boring boots why not get your hp faster and use your feint to block most attacks? To be honest boots with 3 potions are way to common when you use pendant though this makes it harder for your enemy to kill you and also gives you a boost on the warmog.

(3rd item)Guinsoo's Rageblade: To be completely honest this is the only item in the whole build which will make your opponents rage when you have a gunblade with you. Increased attack per attack + the damage increase I mean comon. Op much?

(Rush)Hextech Gunblade: No comment. Its all in the item.

(Late game)Abbysal Scepter: Your going to need a scepter for the ability power and the magic resistance. I wouldnt recommend you getting this mid game or early this is more of a late game item.

(1st High end item)Warmog: Every shen needs a warmog...

Ionian boots of ludicity: This helps you spam your blade and helps you get closer to your opponent by dashing to them every 4 seconds.

Deathcap: Dat ap.

Exaust:Exaust will help you get most of your kills as an AP shen you will need to get alot of kills. Once you get your gunblade there is almost no escape you can either dash and gunblade or gunblade Vorpal blade taunt them and exaust for the kill.
Teleport: Teleport is just to get ganks around the whole map which will come in handy for your build. Yes shen does have his ulti which can teleport but teleport is for when his ult is on cooldown or you have a stranlger minion heading to a tower.

Hello this is my first guide and since I play alot of shen I decided to make my first one on shen. AP shen is almost god mode. you go in with taunt they end up with 3/4 of their hp you throw in your vorpal blade they should have 1/4 of the hp since you have ki strike they try to run? gunblade + exaust. Fient if you get low (usually never happens) you charge there you go. kills all to yourself.