B737-300 CREW WAS CLRED FOR CHARTED VISUAL APCH TO RWY 16L AT SEA WITHOUT HAVING CONFLICTING ACFT IN SIGHT.

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APCH CTL GAVE OUR ACFT RADAR VECTORS IN VISUAL CONDITIONS. ATIS INFO CALLED FOR BAY VISUAL (ACFT ARRIVING FROM W) OR HUSKY VISUAL (ARRS FROM E). THE CTLR DID NOT GIVE US ANY VISUAL APCH PROC AS WE NEARED ALIGNMENT FOR RWY 16R FROM THE W. NEARLY RIGHT OVER THE FINAL APCH COURSE; APCH CTL ASKED IF WE HAD THE ACFT Y IN SIGHT THAT WAS BEING VECTORED FROM THE E FOR RWY 16L ON THE HUSKY VISUAL. WE COULD NOT CONFIRM THE TFC; AND ALMOST IMMEDIATELY WE WERE CLRED FOR THE HUSKY VISUAL APCH. THE CLRNC OCCURRED JUST BEFORE WE WERE ABOUT TO CROSS THE FINAL APCH COURSE AT A 60 DEG ANGLE FROM THE WRONG SIDE FOR THE CLRNC GIVEN/ISSUED. THE CONFLICT OCCURRED SHORTLY AFTERWARDS WITH AN RA. THE CAPT WAS ABLE TO COMPLY WITH THE RA WITHOUT ABRUPT MANEUVERING. BECAUSE OF THE TIMING OF THE RA AND THE NEED TO TRY TO REORIENT OURSELVES WITH THE CONFUSING CLRNC AT THE WORST POSSIBLE TIME; WE NEVER WERE ABLE TO SEE THE TFC. THE WHOLE ORDEAL WOULD HAVE BEEN EASILY AVOIDED HAD WE BEEN SIMPLY CLRED FOR A VISUAL APCH TO RWY 16R. SUPPLEMENTAL INFO FROM ACN 533857: WE WERE ON THE JAWBN 7 ARR INTO SEA; AFTER ALKIA ON VECTORS TO RWY 16R LOC (W SIDE OF LOC); APPROX 16 MI N OF SEA. JUST ABOUT LOC INTERCEPT APCH CLRS US FOR THE HUSKY VISUAL ON THE W SIDE OF THE LOC. WE THEN CROSSED THE LOC AND WERE IN A R TURN TO RE-INTERCEPT RWY 16R LOC. ABOUT THAT TIME WE GOT A TCASII THEN AN RA I STOPPED THE DSCNT; CONTINUED THE TURN (SAW VISUALLY) NO ABRUPT MANEUVERING. APCH ADVISED US OF TFC (ACR) THEN ASKED WHAT WE WERE DOING. I REPLIED HEADING BACK TO LOC VERIFY HUSKY VISUAL. I BELIEVE WHAT CAUSED THE PROB WAS BEING CLRED FOR THE HUSKY VISUAL ON THE W SIDE OF THE LOC. THERE IS NO PROC FROM THAT SIDE; ALSO THE TIME THAT THE CLRNC WAS ISSUED.