Smashed screen on Xperia Z3, need to download data without touch capabilities
I have a phone with smashed screen as well and need to recover photos and videos. Searching around I have found several places where they mention using OTG (On The Go) USB cable to hook up a mouse and keyboard, also you can possibly hook up the phone to HDTV as explained here:
http://androidforums.com/threads/broken-screen-no-backup-and-need-your-data-try-this.841614/

I am yet to try the methods described as I need to buy the necessary cables first.