Get a USB OTG cable, and connect a standard USB mouse to your phone. You can use the mouse on the lockscreen; no need to enable anything in advance.

I tried this with http://www.amazon.co.uk/gp/aw/d/B009DFCCKO and it worked perfectly with my Nexus 5. It took a few weeks to arrive from China, but luckily I wasn't in a hurry. I'm sure it's possible to get something similar sooner if you pay a little more.

To answer the other part of your question, there's no need to reset a device just to replace the screen (I changed the screen on my Nexus 7 without resetting it). But if it was me, I'd feel happier about sending it off for repair if I had all the photos safely backed up, just in case.