Unless of course this monkey knew a thing or two about chemistry.
Do you have particularly indepth knowledge of the components and ingredients in an alkaline battery? So how could you know if it is safe to tinker with? Zinc and Manganese oxides or easily handled safely. I believe that the dangerous part is called Potassium Hydroxide, which, like any other chemical, can be handled with proper gear/equipment and appropriate method. http://en.wikipedia.org/wiki/Potassium_hydroxide
Oh, after review it turns out to be the electrolyte, and is heavily basic thusly yes. This would be the dangerous one. It has a boiling point of 1200 something degrees celsius, and interestingly it has a melting point of about 420ºC, which means it isn't a liquid, and thus it is more then likely dissolved in something to act as the electrolyte.
With the information you can get off the internet, that websites like Wikipedia have, you can safely handle loads of harmful chemicals. Some you can't. If it gives off toxic vapour and has a low-enough flash point it can be quite difficult to handle, often costing lots of money for gear and equipment. Like Gasoline for instance, which has a low flash point, who's fumes are both carcinogenic and explosive.
It's all in how you look at it.
"George Bush says he speaks to god every day, and christians love him for it. If George Bush said he spoke to god through his hair dryer, they would think he was mad. I fail to see how the addition of a hair dryer makes it any more absurd."