Most techs can remove the strings from tuners and reattach them without making a major difference in the sound of the strings, but there’ll be some effect. I accept the fact that they will be affected when I’m doing my own work, and almost always wait until I am ready to replace the strings and do both jobs at the same time.
I have loosened them enough to slide the pick guard off, but it’s not my favorite thing to do because of the sharp pointy things that live underneath it, which can make a mess of the guitar’s finish.
My other concern, whether they are regular tuners or locking, is will the string be kinked or nicked during the process. If so, or I can’t get the strings back on in their original positions, then they’re more likely to break, usually at the worst moment. If I have any doubt about being able to get them back on safely I’ll just replace the set. A string breaking mid song is going to piss me off a lot more than having to buy another pack.