I use so little glue it's not running anywhere so that's not an issue.
With good glue less is always better,and tidier.
For fletching I use Gorilla Ultra Bonder that comes with a small brush, just a shine on the base of the vane or feather is enough with that stuff.
I sometimes remove nocks on carbons if I'm striping old fletch an glue off the shaft, but that's the only time I would touch em' once their in place.
When ever you use glue on any arrow always make sure all working surfaces your going to glue are very clean.
Plastic vanes can have a release agent on them, and carbon and Alloy arrows can as well.
I've always used White Spirits as a cleaner simply because I always seem to have some.
Be very careful with it though, because it burns quite well.