AFTER TKOF B747-400 FLT CREW DEVIATED FROM ASSIGNED HDG WITHOUT ATC CLRNC TO AVOID WX.

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PRIOR TO FLT; DUE TO NUMEROUS CONVECTIVE CELLS IN THE AREA; IT WAS DECIDED TO SET UP WITH FLAPS 20 DEGS; MAX EPR; AND BRIEF FOR THE POSSIBILITY OF WINDSHEAR. WX RADAR WAS THEN TURNED ON DURING TAXI TO RWY 16R. AS WE WERE TAXIING INTO POS; WE WERE CLRED FOR IMMEDIATE TKOF DUE TO LNDG TFC AND TOLD TO TURN TO HDG 170 DEGS. ON TKOF ROLL; IT WAS CLR THAT THE 170 DEG HDG WOULD TAKE US DIRECTLY INTO AN AREA OF RED RADAR RETURN. A SECOND CELL (YELLOW) WAS LOCATED BEYOND THE FIRST ON RWY CTRLINE. AS WE BECAME AIRBORNE; I TOLD FO TO TELL TWR WE WOULD BE UNABLE THE 170 DEG HDG AND NEEDED A 130 DEG HDG TO REMAIN CLR OF THE CELLS; AT WHICH TIME TWR RESPONDED TO CONTACT YSSY DEP. AS I STARTED A GRADUAL TURN TO APPROX 140 DEGS AND AFTER CONTACTING DEP; WE WERE IMMEDIATELY TOLD 'NEGATIVE' AND TO TURN TO 170 DEG HDG. WE THEN TOLD DEP WE WERE UNABLE DUE TO WX; AND THEY AGAIN RESPONDED 'NEGATIVE' AND TO RETURN TO RWY CTRLINE DUE TO PARALLEL TFC ON RWY 16L; WHICH I DID. (NOTE: FO HAD VISUAL CONTACT OF THE TFC AS IT WAS TURNING AWAY. IN ADDITION; I WAS NOT PAINTING ANY CONFLICTING TFC ON TCAS). AT THIS POINT; WE WERE ABEAM THE FIRST CELL AND WERE ABLE TO VISUALLY TRACK A PATH BTWN THE 2 CELLS; BACK TO RWY CTRLINE; IN COMPLIANCE WITH ATC. WE THEN CONTINUED ON A NORMAL TKOF WITHOUT FURTHER INCIDENT. (ONE OBSERVATION: IN RETROSPECT; IT WOULD PROBABLY HAVE BEEN BETTER TO ABORT THE TKOF ROLL IF I HAD KNOWN THAT THE DEV AROUND THE CELL WOULD NOT HAVE BEEN GRANTED. CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO: REPORTER STATED THAT GIVEN THE INTENSITY OF THE WX THAT HE WAS PAINTING ON RADAR; HE WAS NOT WILLING TO FLY THROUGH THE AREA. DEP CONTROL APPARENTLY DID NOT REALIZE THE INTENSITY OF THE WX AND DID NOT APPRECIATE THE URGENCY OF THE REQUEST. HE WAS LATER TOLD THAT PERHAPS YSSY DID NOT HAVE REAL-TIME WX RADAR CAPABILITY; BUT THE ANALYST CANNOT VERIFY THIS.