Dangers of corroded mercury battery
Based on the color alone, the corrosion could be mercury (II) oxide, which is nasty. As with other mercury salts, it can end up in your body in a variety of new and exciting ways, such as by inhalation (that is not to say that elemental mercury cannot do so, it is simply more difficult), which make it more dangerous than elemental mercury. For this reason, do not touch it, even if it ends up being another salt. 

What I (and I am no hazmat professional) would do is search around on the Internet for my local hazardous materials disposal facility (it may go under a different name) and would call them. I would ask them about the battery whilst giving as much information as possible about it, even if it seems unrelated. If (and only if) they ask you to bring it in, do the following:


Wear at least two pairs of gloves while handling it, and only do so briefly.
Put it in several layers of baggage, something that you will be okay with losing; and make sure it will not break.
Bring it in carefully, being sure not to breach the membrane. Also, be sure not to touch anything with the gloves used.


In addition, be careful with any of the tools that it touched, they could also be highly contaminated. If you want to learn more about mercury (II) oxide, the Wikipedia article seems relatively accurate (the same could be said about mercury batteries): https://en.wikipedia.org/wiki/Mercury(II)_oxide

Disclaimer: As stated, I am no hazmat professional, and my advice does not take authority over the advice of a professional.