CE421 FLT CREW ELECTS TO REMAIN AT FL200 WITH CABIN ALTITUDE ABOVE 10000 FEET AND NO SUPPLEMENTAL OXYGEN; TO TAKE ADVANTAGE OF TAILWINDS. CREW REPORTS SUFFERING THE EFFECTS OF ALTITUDE SICKNESS UPON LANDING.

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THIS WAS AN EVALUATION FLT OF OUR PART 135 ACR CERTIFICATE'S ABILITY TO GET EXTENDED RANGE OVERWATER AUTH TO CONDUCT FLTS TO ZZZ FROM HONOLULU/LIHUE; HI. THE FAA NAV SPECIALIST OBSERVER GAVE US NUMEROUS TASKS TO PERFORM; TO DEMONSTRATE OUR ABILITY TO NAV OVERWATER. UPON REACHING OUR TURN POINT; WE HEADED BACK TO HNL (VIA LIHUE). OUR CABIN PRESSURIZATION WAS MALFUNCTIONING DUE TO A LEAK IN THE NOSE BAY ELECTRONIC HARNESS HOLE THROUGH PRESSURE BULKHEAD. OUR CABIN CLBED ABOVE 10000 FT AND WE FLEW ON WITHOUT SUPPLEMENTAL OXYGEN FOR 4 HRS. THIS DEGRADED MY JUDGEMENT AND I BELIEVE MY BLOOD OXYGEN WAS DEFICIENT. I CONTINUED OUR FLT AND MAY HAVE FAILED TO RPT CANON INTXN -- WE ESTABLISHED VHF RADIO CONTACT SHORTLY AFTER PASSING CANON; WITH HLF. IN THE FUTURE; I WILL DSND TO HEAVIER AIR. WE HAD NO SVCABLE OXYGEN ON BOARD; AND CHOSE TO STAY HIGH TO UTILIZE TAILWIND BENEFIT TO EASE OUR RECOVERY TO HONOLULU. I HAD A HEADACHE DUE TO ALT SICKNESS UPON LNDG. BUT MY CONCERN FOR OUR DIMINISHING FUEL STATE OVERRODE MY DECISION TO DSND.