like the others have said, if you love Zachary, then use it. I'd talk to the other parents first and tell them to be honest about how they would feel. For me it would depend on how often the kids were to be together and how close you were to the family as to whether I would use it or not.
Of your other names I only like Oliver. I havn't heard it all that often. i have a cousin named Olivier (o-liv-e-ay). French version of Oliver (his mums french). i like the name, but people get confused at the spelling so when they read it they say Olivia, like a girl.
Gabriel is a bit girly, but I know girls named Gabrielle, so thats why I think girl. And Wilder is a bit out there for me. I love Wil as a name though.
Good luck