If you resort to dremeling anything, cut off the metal tabs from the battery to get it out while leaving plenty of metal for you to grab when you go to desolder the tabs from the MB.
Once you get your MB free, throw the entire MB into a tub with denatured vinegar (aka "white vinegar") and let it soak for a few hours (how long you will need to let it soak is dependent on how much the battery had leaked). Use an old battery-powered toothbrush to scrub down the board. Once you are satisfied that the alkaline has been cleaned off of the board, rinse the board off really well, I use regular "city water" for that. Then shake the water out. It takes a lot of shaking, those edge card connectors will trap a lot of water. Then immediately, and I mean immediately, set the board next to a space heater and begin a 2 - 3 day drying process. In other words, be sure that it is dry, and don't get into a hurry.
I've done this to all of my 2000's and 4000's (about 7 or 8 MB's total) and haven't had a problem. I've done it to nearly all of my A500 memory expansion cards (a lot of them), but screwed up and didn't dry them off (I let them air dry). The boards are fine, but the metal covers now have surface rust.