|Vine will die. Oil will still be active for many years in the vine.
Wash the outside of the walnuts and you should be fine. Urushiol oil can be washed with ease from object but once it binds to our skin - that is where it becomes a challenge. There is a paper on this site discussing this and the challenge of breaking the bond to release and wash away the oil. Because this oil is usually beneath having penetrated your top layer of your skin like any lotion or oil, it goes unnoticed until our bodies immune system takes action... rash, itching and oozing.