This may or may not be well known. Either way, I don't want it to be as well known as it would be if posted publicly.
The way to dye your weapons is simple:
Type that into Neverwinter.
You'll come up with a window looking a little like this:
Simply choose your weapon, and dye:
And then you're done.
Picture for reference only. Note, I used a dye pack, so individual colour dyes (such as black, blue, etc) you will need to fill in appropriate spots such as Primary, Accent, Secondary. It dyes all of the weapon (from what I've tested) not just the hilt. Some weapon enchants will completely over-power the dye so you wont be able to tell, so keep that in mind.