If you leave the shaft in there it can rattle around and cause some damage, so that's the important thing to get out.
You could then "plate" the hole or simply put the pump back to keep the cooties out.
OR
You could leave the entire assembly alone and simply connect a tube between the in/out of the pump. If you fill the pump with oil it will run there fine all by itself doing essentially nothing.
OR
If the pump is working, why not just leave it alone?
Oil pumps get blamed for all kinds of problems but they are rarely the cause.
They can't kill an ignition component, they don't cause an overheat, they don't clog carbs - if a single cylinder or piston gets toasted that was likely a dirty carb, not the oil pump - if it fails all your cylinders will fry.
Even if it's busted (rare), a new pump sells for under 100 bucks at a dealer. The problem with this system was the early drive gears, but that was corrected making this a good system.
The VRO2 pump on my OMC retails for about 400 bucks. I still have it in place (and working perfectly) on my 1986 model. If it ever goes, a new one will take it's place.
Oilers are not the "boogey man" that guys at the dock would have you believe.
And finally, if you do disable it you can no longer blame it for any future problem your power head has
If you really would sleep better at night with it gone, then get rid of it. But if you simply think it's the "thing to do" because "Bob" says so, I would ask a few more guys who actually rebuild motors for their opinion - most will tell you the oiler is one of the least likely points of failure on an outboard...
