Yes, you can support efforts to preserve remaining habitats and examples of that wildlife and conserve the cultural heritage of the victims. Or at least you could avoid actions that might hinder or prevent such efforts, such as by not voting for representatives that might de-fund them or pass laws hindering them.
Nobody's suggesting you should be tried for the crimes of your ancestors, or previous members of your society. What we can do is stop doing more damage and try to rectify some of it, where it is reasonable and affordable to do so.
I disagree. While I think your suggested actions are reasonable, nothing distinguishes them from actions we would take if our hands were clean, and instead another group were at fault.
I think it's just a matter of degree. I feel a general responsibility towards planet earth in general to preserve its environmental and cultural heritage. But I feel a greater obligation to contribute towards mitigating some environmental and cultural harms than I do towards others due to my nation and cultures role in exacerbating them.
There's no law at work here though. If there is some specific issue you are particularly concerned about that happens not to have any such historical link to you, but it bothers you so much that you take a special personal interest in it then that's fine. But even without dedicating our personal resources towards righting the worlds wrongs, as tax payers, consumers and voters we often make decisions that bear on these issues. I think it's worth bearing that in mind.
Nobody's suggesting you should be tried for the crimes of your ancestors, or previous members of your society. What we can do is stop doing more damage and try to rectify some of it, where it is reasonable and affordable to do so.