All I know about willow trees is this (below) so I'm not sure it's totally pet-safe- might be better off to coat it with a "no VOC" pet-safe waterproofing product,
though I doubt that enough salicin could rub off on a snake (it probably has to be boiled out) but I'm not sure I'd take the chance? You could also wrap the
branch with something (like that colorful compression wrap used for sprained ankles & such) to prevent too much contact, just in case?
The active ingredient in the medicine made from willow bark is called salicin. Some people use willow bark as an alternative to aspirin, particularly those that experience chronic headaches or back pain. ... It comes from the branches of 2- to 3-year-old willow trees.