detergant, and a brush? hmm its not like you can nutralize it with acid and improve the situation, but if you dont have metal surfaces, vinegar or vinegar and water mix would nutralize the alkaline (acid).
i think i would just clean it up normally, then lightly abrasion the metal contacs needed to connect to the batteries.
i think that is correct that the substance inside is a "base" an alkaline , but it is only lead acid batteries that i would bother to use a nutralizing agent.
if you use even a light acid in there, you could make a worse corrosion than what you have now.
and the part about not getting any on you , would still apply.
for the rust, just silicoln spray the insides after a cleaning the gunk out, and after sanding the contacts, to stop any further rusting. silicoln spray like the stuff in the yellow can, is a very light oily silicoln with a lot of high volitile solvent.
so it will put a light protective mask on, unlike wd40 which will put a mess in there.
Alkaline cells have in them ... an alkaline substance or base.
To neutralize a base you use an acid. Ordinary household vinegar will work in this case (don't use the good balsamic for this!), or some cola soda. Swish in, and then rinse well!!!!
If you have a SLA or unsealed Lead-Acid battery leak, then you use plain old baking soda to neutralize the acid. Again rinse well afterwards. Don't get any baking soda or rinseate into the battery though.
Once the chemicals are flushed out, then you should remove the corrosion (rusty gunk). Flush out, rub softly, rub harder with a mild abrasive substance (think Scotch-Brite pad), if that doesn't work you can pretty much give up.