Transfer data from old iPhone to new one

So I have an iPhone 6 with IOS 9 software. The phone is super glitchy and seems like it’s going to die any day so I bought a new iPhone 7 Plus and I want to transfer all my data from the iPhone 6 to the 7+. The problem is iCloud doesn’t work since the software system is outdated and I don’t want to risk updating till I back up my phone. I tried backing up through iTunes on my Mac but I don’t have enough space. I bought an external hard drive but I don’t know how to do the iTunes backup through the hard drive, the only option it gives me is to backup to the computer, which I don’t have enough space for. Does anyone have any ideas on how I can transfer all my data from the iPhone 6 to the iPhone 7 Plus?