Just pick them, and wash your hands before and after. Then put your boogers in a trashcan. I always wrap a piece of toilet paper around my finger when I pick my nose.
If it's hard to get them by picking, I use pliers in front of a mirror and then put the boogers on a piece of tp which I then throw into the toilet or trash. (Remember that if you use pliers, you need to be careful so that you don't stab yourself with them. Also wash your pliers before & after.)
I wouldn't put toilet paper up my nose - I don't trust other toilet users to not touch the toilet roll and I don't trust the room to not have fecal particles from lidless flushing on things. I don't want tu put someone else's poo up my nose.
Well, perhaps it might be possible to catch some tummy bug from someone else, I don't know, but you inhale the fecal particles when you flush anyway I suppose.
The lid stays down all the time (well, in between use) at our house, with the idea that you minimise the amount of fecal particles floating around your room. I know it doesn't eliminate it, but I want to flush as much as possible of the poo and not inhale it, so I insist on the lid being closed.
I'm not claiming danger, I just don't like the thought.