Well i have used a solution called Wheel Bright on my very dull rims on my old truck and it brought them back to life,i also used something from meguires products i will find out the name of it later and post again,but i was happy with the Wheel Bright it is a spray so its easy.
That oxidation is protecting the metal and you can leave it. However, I did use meguires aluminium wheel cleaner and a buffing wheel on my crab skiff and it shined.... too much so. I then went to a green Scotch Brite pad and the mequires wheel cleaner and got just the look I wanted. Its a bright scuffed finish.
OK, what does the length of the handle have to do with shine??
Problem is anything that will make it shine will surely remove the finish (if any) and you will be dull again within a few launches. I would leave it alone or just wash with best cleaner you can find with minimal effort.
You can try using a baking soda mixture the consistency of cake icing, apply, allow to dry then remove gently with a wet Scotch-Brite pad.
Sodium bicarbonate is a mild abrasive and easy to rinse off