Lead ain’t that dangerous. Just take it out and dispose of it like you do with normal batteries. Clean your hands afterwards and you’re dandy. As for the clock, the battery contacts, and whatever they were attached to, are likely eaten away, but I can’t say that for certain from this photo. If you’re lucky and they’re mostly intact, some IPA scrubbing and a dip in vinegar, and a bit more scrubbing, should take most of the crust away. That rust though, probably some vinegar, maybe a deoxidating agent (like navy jelly?) could clean it off. Even cleaning all of it doesn’t guarantee that it’ll work any way.