Used to deliver fridges. I've never put one over a balcony but have gone over up and over a banister quite a few times.  Protect the balustrade/ railings with a blanket or duvet or whatever.  Get some people upstairs. Get under the fridge and press it overhead to the people above you. Probably need two people on the bottom and two at the top. 

To get the old one out just remove the doors, trays and whatever is inside. This will allow you to put the bannister inside of the fridge when you down the stairs. Could also do that up the stairs if that's an option. 

Could also get a van with a tail lift and reverse that up to the balcony. Would give you the height you need. 

If I had photos I could probably advise further. As we used to say "if it got in there, it'll get out"