First off, in order to use this mod you'll need to change the following line in your Fallout4.ini which you'll find in "Documents\My Games\Fallout 4"

from:
"sResourceDataDirsFinal=STRINGS\"

to:
"sResourceDataDirsFinal=STRINGS\, textures\"

then place (unzip) the textures directory into your fallout\Data directory

the appropreate files are under:

textures\actors\character\character assets\facedetails

they are:

(filename) (stock tattoo) (new tattoo)
factat01_d.dds clover and wishbone
factat02_d.dds eagle                becomes    pink faun
factat03_d.dds radiation skull        becomes    fox
factat04_d.dds badluck horseshoe        becomes    snow cat
factat05_d.dds anchor                becomes    full pink faun
factat06_d.dds A-
factat07_d.dds D-
factat08_d.dds -
factat09_d.dds :

you'll also find:

_facePaint_fox.dds
_facePaint_fullfaun.dds
_facePaint_pinkfaun.dds
_facePaint_snowcat.dds

but the game won't use these and they are just there to make life easier if you want to replace a different tatto with a different animal face.

I tried to mod face paint first, but tattoos are full color with alpha so it was much easier to do, unfortunately this means you'll need to find at least one tattoo in the game before you can use it, and they aren't super common.