LIFEGUARD SMT TRACK DEVIATION AFTER TKOF.

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AFTER CALLING FOR TKOF CLRNC; I WAS CLRED TO 'TAXI INTO POS AND HOLD.' I WAS ALSO GIVEN A WAKE TURB ADVISORY FOR THE ACFT THAT WAS TAKING OFF IN FRONT OF ME. SHORTLY THEREAFTER I WAS CLRED FOR TKOF. I DID NOT HEAR THE TWR SAY; 'MAINTAIN RWY HDG.' AFTER TKOF I TURNED RIGHT 30 DEGS TO INTERCEPT V169 SWBND FROM RAP. AFTER DEP; DURING INITIAL CLB; ELLSWORTH APCH CTL GAVE US A TFC ADVISORY FOR TFC AT 12 O'CLOCK AND 1 MI. SIC ASKED THE CTLR TO 'SAY DIRECTION OF FLT;' AFTER REPEATING THE ADVISORY. THE CTLR REPLIED; 'YOU WERE TOLD TO MAINTAIN RWY HDG. TURN RIGHT HDG 200 FOR VECTORS AROUND TFC. WERE YOU INSTRUCTED BY TWR TO MAINTAIN RWY.' I INSTRUCTED MY COPLT TO REPLY; 'NOT THAT WE RECALL.' SHORTLY THEREAFTER MY COPLT SAID TO ME; 'HE DID GIVE US RWY HDG. I SHOULD HAVE SAID SOMETHING WHEN I SAW YOU START THE TURN.' WE NEVER SIGHTED THE TFC; NOR WAS EVASIVE ACTION NECESSARY. AFTER BEING VECTORED BACK ON COURSE; I REPLIED TO THE CTLR; 'SORRY FOR THE CONFUSION.' THE SITUATION OCCURRED DUE TO MY FAILURE TO HEAR THE ENTIRE TKOF CLRNC FROM THE TWR AND THE COPLT'S FAILURE TO SPEAK UP WHEN HE SAW MY MISTAKE. TO PREVENT A RECURRENCE; I WILL LISTEN TO THE ENTIRE CLRNC AND INSTRUCT MY COPLT TO CORRECT ME WHEN I'M WRONG.