I agree with just about everyone's replies here.
Before going with any of the suggestions I think you need to share what type of paint was used and how extensive the runs are.
The nib files work great but it might be difficult to use them on a whole line of runs.
Also, for a nib file to work best, the paint needs to be pretty hard or you just start to gum things up.
Nothing is going to work well unless the paint is hard, really hard.
Unless it was 2 part, I would wait at a minimum of 2 weeks, depending on how thick the paint was applied. But like Finding41 says, it can really take much longer than you would imagine.
In a inconspicuous place, press the paint with your fingernail. If you can leave any mark or depression at all I would wait longer. Keep in mind the run is the thickest part of the paint and will take the longest to get hard.
If the paint was 1 part, it can feel dry and hard, but under the top surface, it can still be quite soft.
What ever method you use, nib file, wet or dry sandpaper, if the paint is not hard all the way through you'll break through the top layer to the softer paint and have a real mess. Maybe localized, but a mess none the less.
I think the nib file is great for small, very localized runs, like one drip runs here and there.
If it's an area of runs, I would wet sand verrry carefully with a hard pad as a backer. That way you're just hitting the high spots and not the surrounding area. I would start with maybe 400, then 600, then 1000, then maybe 1500. Using water to keep the paper from loading up.
The secret is having the paint really hard, and taking your time. Don't get impatient and start applying pressure and "scrubbing" back and forth.
Go slow and use a very light touch. Stop frequently and check your work. Make sure you're just sanding the high spots.
To do it right will not be a quick process.
The type of paint might give you some more accurate answers, but that's the basics.
Good luck,
rob j