I'm not exactly sure what you're thinking of doing. If the stab is very thin, you won't have room for a 1/4" tube.

I would remove the LE, drill a horizontal hole throught the vertical fin and replace the LE with a CF tube the same diameter as the thickness of the stab (If the stab is 1/4" thick, use a 1/4" tube) then use filler to get the shape back and re-cover with black (The black may have to extend slightly further aft than it does now to hide the work)