Trimming Cypress

Hello,

I have a line of Cypress, 10 feet high in a north east facing garden. My neighbor have been trimming them properly over the years and they are nice and green on his side. My side is a different story. It looks like they have not been trimmed for long time. They are 8-10 feet wide on my side and while the external 2-3 feet are green, the internal branches have no leaves and just look brown.

I would like to trim my side to a width of 3 foot. My question, if that would it "kill" the trees and would it be green again (and how long would it take).  My hope is that the fact that the green side of my neighbor will stay untouched, can help. 

Many thanks for your help !