
You need a wrench similar to this one: http://cgi.ebay.com/NEW-Pro-Watch-Repai ... dZViewItem
If you go to ebay and type in "watch repair tools", you will find a host of very inexpensive tools that form the basics of beginning watch repair.
Cleaning the switch contacts may be all that is needed to fix your problem. Sometimes bending the contact on the module a bit closer to the pusher can help as well. If you do use dielectric grease, err on the side of conservative; a little goes a long way.
The LR44 batteries will work fine.