this info is assuming its alkalines that leaked.
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.