First of all, drilling a hole will function as a significant stress riser. It is a good generality that stress around the perimeter of a hole is 3 times the stress in the surrounding metal. If this rudder was designed to handle the stress it sees without any holes then you should not not assume that increasing stress is acceptable.
Just fill the hollow part of the tube with oil. It is an absolutely effective way to protect against corrosion
. And it is free.
If you don't like the oil for some reason then another approach is to weld on a cap at the end of the shaft. This will seal the tube ID. With the oxygen available for corrosion limited to what is trapped inside the tube corrosion will be positively stopped.