I have to be honest, I would immediately remove my daughter from the bassinet, until you get a DEFINITIVE answer about the existing hazards of the fumes or not. Would you want to sleep in a bed in which you could smell polyurethane all night long? Your baby can't tell you she is smelling it and breathing it in but you can be sure she is.
Read the warnings on a polyurethane container, there has got to be some kind of initial warning to stay away from the fumes for a period of time before it dries. What's behind those warnings?
Some time ago my parents gave me a set of painted hardwood blocks that my Dad used to play with when he was a child. I was really touched and loved watching my son play with them. Then a little voice in the back of my head said, wait a minute, paint from 75 years ago, it's got to be lead based! It is said even lead paint dust can somehow harm a child's neurological development. I'm not looking forward to telling my parents he can't play with them any longer, but HEH! what's more important my babies neurological development or my parents feeling a little hurt, they'll get over it!
It's the thought that counts and obviously your Dad put a great deal of love into constructing the bassinet, let him know that you know that.
Your instincts are talking, listen to them.
In your babies best interests,
N.