There is no way to exclude data from a shared family tree. If I needed to do this, I think I would maintain two copies of the tree. One complete copy for myself, and one copy with the limited information to share.
As you probably know, you can export your GEDCOM file and then import it as a new family tree. If this is a large tree, then you can probably save a fair amount of time by editing the GEDCOM file before you upload it.
What information do you want to exclude from the shared version?