PLT OF A PA23-250 AZTEC LOSES CTL OF ACFT ON A XWIND LNDG AND DEPARTS RWY AT TEB; NY.

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IMMEDIATELY FOLLOWING TOUCHDOWN; THE ACFT WAS FELT TO 'HIT' SOMETHING ON THE RWY (I BELIEVE IT WAS A RWY CTRLINE LIGHT). THE LNDG FOLLOWED A MODERATELY TURB; BUT STABLE APCH; AND THE LNDG WAS ACCOMPLISHED WITH A CONSIDERABLE XWIND ON THE RWY IN USE (RWY 19) (WIND APPROX 250 DEGS/12 KTS VIA WIND CHK ON SHORT FINAL). THE LNDG WAS PERFORMED IN A NORMAL XWIND SLIP; WITH THE UPWIND MAIN TOUCHING FIRST; SLIGHTLY BEFORE THE DOWNWIND MAIN; FOLLOWED BY THE NOSE GEAR; WITH XWIND AILERON APPLIED AFTER TOUCHDOWN. WHEN THE 'HIT' OCCURRED; (THIS WAS RPTED BY ALL PAX); THE ACFT VEERED L OFF THE RWY ONTO THE GRASS MARGIN. THE SOIL WAS VERY WET; AND THE ACFT SANK INTO THE MUD COMING TO REST UPRIGHT ABOUT 30 FT FROM THE RWY EDGE. THE ONLY APPARENT DAMAGE WAS ON 1 WING FLAP; WHICH HIT 1 OF THE RWY EDGE LIGHTS; CAUSING A DENT IN THE UNDERSIDE SKIN OF THE FLAP. WHEN THE ACFT VEERED L; I REACHED THE POINT WHERE I FELT I WOULD NOT BE ABLE TO STRAIGHTEN OUT THE PATH WITHOUT PUTTING THE ACFT AT RISK OF TIPPING TO THE SIDE; SO I DECIDED THAT THE SAFEST COURSE OF ACTION WAS TO ALLOW THE ACFT TO CONTINUE ON ITS OWN PATH; DISSIPATING SPD; AND KEEPING AS MUCH ST AS POSSIBLE OFF OF THE NOSE GEAR. THE SKID MARK LEFT ON THE RWY SEEMED TO INDICATE THAT AFTER TOUCHING DOWN; THE MAIN GEAR 'LIFTED' SOMEWHAT; AND WERE NOT MAKING SUFFICIENT CONTACT WITH THE RWY TOPROVIDE ANY BRAKING ACTION. IN THAT CONDITION; THE STRONG XWIND WOULD HAVE BEEN ABLE; AND APPARENTLY WAS ABLE TO PUSH THE ACFT SIDEWAYS; STARTING THE CHAIN OF EVENTS LEADING TO THE OFF-RWY EXCURSION. MY ONE THOUGHT AS TO A POSSIBLE CORRECTION TO THIS EVENT IS THAT IT WOULD HAVE BEEN BETTER TO HAVE HAD THE LNDG ACFT USE RWY 24 AT TEB; WHICH WAS ALMOST DIRECTLY ALIGNED WITH THE PREVAILING SURFACE WIND. HAD THIS BEEN USED; ONE OF THE MAJOR LINKS IN THIS CHAIN OF EVENTS; THE STRONG XWIND; WOULD HAVE BEEN ELIMINATED; LIKELY PREVENTING THE INCIDENT FROM OCCURRING.