The best way to avoid the discomfort of taking a tampon out dry is to wear the right absorbency for your period flow. If you haven’t quite started yet but think your period is on its way, wear a liner until you see the first trickle and then use the best absorbency tampon for your flow. Same goes at the end of your period as your flow tapers off. It may be better to wear a liner if it is hurts to take out a dry tampon. For sure, tampons aren’t meant for every day sort of discharge, they are WAY to absorbent for that and it will hurt every time you take it out. But to answer your question, there’s no harm in peeing a little as you pull out the tampon and sometimes relaxing your muscles enough to pee may also relax them enough to take the tampon out more comfortably.
I have personal experience with this one. There have been lots of times when I used a tampon toward the end of my period (about 5 days into it) and it’s simply not catching a great deal of blood. In hindsight, I should have used a panty liner on those days because it was so minimal. So, I have experienced this same dryness when trying to take out a tampon and I have done exactly what you’ve done – pee through the tampon before removing it. It worked because there was enough moisture to avoid some of the pain of a dry tampon. You may already realize this, but you can pee using a tampon anyway so doing it before removing it is perfectly fine.
Ah, yes. The old dry tampon removal. I've dealt with it plenty of times! As far as strategies to minimize the discomfort, I think it would be fine to pee with your tampon in if that makes it easier for you to remove afterwards. I've definitely kept my tampon in while peeing, but it doesn't usually get too wet from the pee (and I think that's a good thing!). Another way to avoid the dry tampon feeling is to use the very smallest /lowest absorbency tampon possible for your flow. That might mean starting with the tampons meant for light flow days -- they're pretty tiny -- and working your way up as needed. If your tampons are regularly pretty unused when you remove them, they're probably too big/high absorbency.
This is not intended to be medical advice. Everybody is different so please make sure to consult your physician if you're having issues. Do not delay or refrain from seeking professional medical advice from your physician because of something you have read on this site.