You don't have to put a skin on LFSW to use it; it just has to be there for others to automatically download it when you use it online.
To make a skin work in LFS, put it in your LFS/Data/Skins folder. Make sure it has the proper 3 letter prefix followed by an underscore (eg. XRT_skinname.jpg for an XRT skin). Select the car in game. While in the garage, click "NEW" in the colours section on the left hand side.
Enter a name for the colour set and click OK or press Enter. On the bottom, click the 'Colours' tab. Click on the skin name, and select the skin from the list. Modify the car body colour with the sliders to get a white body if not already white.