Chosen Solution

I’ve been fixing iPhone for a couple of years now and I always shut the phone down before repair but I usually never disconnect the battery. Would it be smart to disconnect it before every screen replacement?

I’ve never had any issue, and I’ve been doing it for years. I’ve even done it a fair few times forgetting to power the device off and it’s been fine. But I would always highly recommend removing any source of power. :-)

absolutely 100% yes. no doubt about it.

I would second disconnecting the battery. While you will probably be fine in most cases, do you really want to risk damaging the device, by skipping a step that takes a few seconds.