I have been dealing with the cleaning of alot of aluminum parts latley and many are very badly oxidized.
Steel wool I find to be contaminating in many ways (the adverse effects on aluminium and the "shedding" of it all over my bench and work space)
What I have been using for aluminium parts is;
sand paper (600 - 1200 grit depending on the condition of the part) the black waterproof kind and wetsand the piece with 600, then 800 and so on up to 1000 or 1200.
Scotch Brite - Home depot sells this as "Synthetic steel wool" in different grades to mimick 000, 001, 002 etc. I also use this with water and it lasts much longer than steel wool and does a great job.
rubbing compound
Mothers aluminum polish.
I get great results from this method and get parts to a almost chrome sheen without contaminating any other projects, tools, parts, etc. with steel wool hair.
Some parts will not require the sand paper / wet sand step but it sure cuts through bad oxidization well.
hope this helps