Human scent won't bother them. straighten the nest and everything but the dead one back in.

https://www.livescience.com/33620-baby-bird-touch-mother-abandon.html

However, after straightening up, do stay away, so things calm down.

Do what ever construction is need to make the nest secure, the parents will probably not object. This seems the best way considering the alternative of doing nothing.

Many years ago we visited my parents who were in their 70's at the time. He proudly showed us how he had reconstructed the dove nest outside the living room windows. The doves were quite happy with his work.

Very few birds have any sense of smell :-) Just try to reposition the nest with all viable occupants as close to where it was as possible. Then keep your distance.