Getting poison ivy off trees

I have several trees in the woods at the edge of my yard where my son plays. I'm putting up some rope bridges (2-rope postmans) but at least one of the ideal trees had poison ivy growing up it. I've removed what i could reach of the vine but of course there are teeny tiny fibrous tendrils and the oils themselves.

Is there any way to render the trunk safe to touch? Soapy water? Some other tree safe degreasing agent?

A wire brush might get the little bits if the bark is thick enough not to damage the tree.

Based on this I decided to try warm soapy water and a broom. Once it's dried I'll try to go pick any remaining bits off and hit it again with soapy water. I really only need to get it within reach of the kids... and figure out how to dispose of the stuff. I know you can't burn it.