PVT PLT OF AN SMA SEL TOOK THE WRONG TAXI RTE AFTER RECEIVING TAXI CLRNC.

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AS A TRANSIENT PLT; I WAS RELATIVELY UNFAMILIAR WITH ARPT. WHEN CALLING FOR TAXIING INSTRUCTIONS AND IFR CLRNC; I WAS TOLD TO TAXI FROM FBO (ADJACENT TO RWY 16/34) VIA THE AUX TXWY; TANGO; TO RWY 34; CLRED TO CROSS RWY 29. (THE CTLR EXPECTED ME TO TURN R ON TANGO AND PROCEED TOWARDS THE RWY 11 DEP AREA.) SINCE I WAS HOLDING SHORT OF 16/34; AND TANGO WAS RIGHT IN FRONT OF ME; AND GND CTL WAS COMBINED WITH DELIVERY ON THE TWR FREQ; AND NO OTHER ACFT WERE IN OP ON THE ACTIVE (NO INBOUND ILS TFC OR POS AND HOLDS); AND THE MOST DIRECT RTE (IN MY OPINION) WAS TO TURN L ON TANGO AND PROCEED (ACROSS RWY 16/34; IMMEDIATELY IN FRONT OF MY POS) DOWN TANGO AND ECHO; WITH CLRNC TO CROSS RWY 11/29. THE CTLR WAS ANTICIPATING THE OTHER RTE TO RWY 34. I BELIEVED THAT I WAS CLRED ACROSS 34 VIA TANGO. OBVIOUSLY; THERE WAS SOME CONFUSION. WAYS TO HAVE POSSIBLY AVOIDED THE INCIDENT: A CLRNC AS 'VIA THE AUX TXWY; R TURN ON TANGO...' OR 'VIA AUX TXWY; TANGO; HOTEL; EXPECT INTXN DEP FROM HOTEL... (WHICH WOULD HAVE MADE ME LOOK FOR HOTEL; AFFIRMING THAT HE WANTED ME TO TAKE THE LONG WAY AROUND). FROM FBO; ACCORDING TO THE NOS ARPT DIAGRAM; THE ONLY EXIT IS VIA RWY 16/34. THE AUX TXWY IS ACTUALLY A DIRT PATH OFF OF THE S TXWY. HOWEVER; THIS TXWY IS NOT SHOWN ON THE CHART. AS AN UNFAMILIAR PLT TAXIING BY THE NOS ARPT DIAGRAM; I ASSUME ANY VALID CLRNC MUST INCLUDE PERMISSION TO CROSS RWY 16/34. ADJUSTING THE DIAGRAM TO INCLUDE THE AUX TXWY MIGHT HAVE MADE ME ASSUME THAT I STAYED TO THE S OF THE ACTIVE RWY. I MUST ADMIT; IT FELT WEIRD XING THE ACTIVE; BUT I WAS TALKING ON TWR FREQ. FOR ME; I HAVE LEARNED THAT IF AT ALL UNFAMILIAR WITH THE ARPT; I SHOULD ASK FOR PROGRESSIVE TAXIING INSTRUCTIONS. ALTHOUGH AT A BUSY ARPT LIKE HPN; THE CTLRS WERE CURT AND UNPLEASANT WHEN ASKING FOR PROGRESSIVES IN THE PAST AT HPN. I GUESS FOR SAFETY'S SAKE WE ARE BETTER OFF WITH A PROGRESSIVE (RATHER THAN A RWY INCURSION).