Don't get hung up on the whole "The weight by volume by which the NIC offsets the PG concentration by it's displacement of the base divided by concentration of the raw NIC metric value thingie".
Explinations can get so convoluted that it blurs the whole simplicity of what you want to do and you'd never notice the difference..
Just pour out 5mls of your 18mg NIC solution then add 5mls of VG shake it up and you have 10mls of 9ml 50/50 unflavored juice. See how simple that was.
I agree completely, although there appears to be a typo: "10 mls of 9 ml 50/50 unflavored" should be 9 mg, yes? For work, I deal with the minutia of accounting for everything to calculate precise quantities and concentrations, but for my juice, +/- 10% nicotine concentration is not something I worry about. I shoot for 33 mg/ml nic, but will end up ranging from 30-36 mg/ml if it makes my measurements easier.
And as far as I can tell, the general convention in the e-liquid industry is to ignore the volume contribution of the nicotine, since at normally vaped levels, it ends up being less than 3% of the total mix. So if you want something to be similar to the stated concentrations in commercial juice, you can ignore the volume of the nicotine (but not the volume of the PG/VG in the nic base, of course).
If you enjoy complex mathematical calculations for the sake of mental exercise, go ahead and include the volume of the pure nicotine. But if not, then do it as dannyv45 describes.