Steve brings up another good point here.
I will have to research these woods in their live forms.
I know for instance that Ficus is toxic when used dead, but live ficus itself is not dangerous, although the milky white sap is an irritant. All locust, yew, and cedars are dangerous live or dead. eucalyptus is can cause problems when live. There are quite a few woods, like oak, that are harmless when used live.
I'll see what I can dig up on live cypress. I suspect the outer bark could be an issue.
Edit: I just did some poking around and the turpenines ( that's a fancy word for turpentine type stuff) in cypress are very dangerous to amphibians. As suspected, even the outer bark of these plants can be risky. It does appear that the risk associated with live trees and contact is very low, however any risk of ingestion or inhalation of the various phenols and turpenines released by the bark could be harmful. However, as of yet I have been unable to come across anything definitive on live cypress. dead cypress is definitely out.