Yes, it should be. The real concern is about WHY the other baby died and if it could have a contagious illness that might spread to its nest mates.
You really don't have to worry about the parents "smelling" you on the baby and rejecting it- that is a myth. However, the latex gloves are a very good idea for YOUR safety. Always practice good hand-washing whenever handling wildlife, especially if there is a concern about illness or disease.