if your overlap and wood chopping script is in the tree then thats even easier. eliminate the extra collision on the characters head then just add a small collision to the tree. from there i believe you just have a input issue. to solve this you just need some script to enable and disable input for the tree bp. below you will see an example of how to do this. just substitute the cast to the class of your player, or instead of the cast use a get player character → equal == → branch combo and connect the other pin of the equal to the other actor pin.
