I've never created a race myself and have no big clue 'bout the mechanics but after a quick look in CK...
isn't the Race linked to the skin (that works like armor) which contains body parts - like the tail?
... so maybe if you duplicate the skin, delete NakedTailArgonian and link your new race to this one instead the original version with tail?
In worst case you could always replace the tail model with an invisible version or downsize it to 0% and link your skin form to it (like i did below) - BUT that's an out of the box idea, quite sure it's doable in CK as well
UPDATE: I just tried the above mentioned CK version, deleted NakedTailArgonian in the skin form and it worked ingame.
Edited by ghosu, 13 March 2014 - 08:53 PM.