You will regret cutting into the anchor locker. That space is not dry and will allow for water intrusion. You may not even be able to fit a unit in there as the space narrows to a point. Additionally the vibrations from waves it at it peak up there and it would require tremendous support and the cooling system may not take well to the abuse.
As others have said - either get a portable that drops in the hatch, a small rolling portable that vents out or install a marine grade unit. Installing a marine unit will require a bottom thru hull for water pickup, a strainer, a pump, the AC unit an control box and finally a side thru hull outet for the water. You will still need to route waterlines 120VAC electric, 12VDC control and power lines and install a thermostat control. I would make a great off season project if you are handy but will be expensive and unless you plan on keeping the boat for a while you probably will not a tremendous increase in your boats value.
-Kevin