SMT MIL ACFT ON NDB APCH HAS NMAC WITH SMA AS IT BREAKS OUT OF CLOUDS ON FINAL.

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DURING AN INST APCH (NDB) TO HAMILTON COUNTY ARPT (HAMILTON IS UNCTLED WITH CTAF); OUR RADAR SVC WAS TERMINATED AND WE WERE CLRED FOR THE APCH AND CLRED TO THE ADVISORY FREQ. WE ATTEMPTED RADIO CONTACT WITH HAMILTON ON CTAF AT LEAST 3-4 TIMES WITH NO RESULTS. WE HEARD NO OTHER RADIO TRANSMISSIONS. UPON BREAKING OUT OF CLOUDS AT MDA; I SPOTTED THE END OF THE RWY APPROX 1 MI AWAY; AT ALMOST THE SAME INSTANT I NOTICED AN SMA AT OUR 12:00 AT OUR ALT IN A CLBING L TURN. I SHOVED THE YOKE FORWARD TO HOPEFULLY DIVE UNDER THE ACFT AND THEN I EASED BACK ON THE YOKE TO TRY TO AVOID SWINGING THE TAIL OF MY ACFT INTO THE SMA. I DON'T THINK THE SMA SAW US BECAUSE THERE WAS NO CHANGE IN HIS PITCH OR BANK ATTITUDE AND NO RADIO TRANSMISSIONS MADE. WE LANDED ON RWY 11 WHILE THE COPLT WAS LOADING OUR PAX AND BAGGAGE. I CONTINUED TO TRY TO CONTACT HAMILTON ADVISORY ON CTAF FREQ THINKING WE POSSIBLY HAD A BAD FREQ. ON THE FOURTH TRY; A YOUNG LADY ANSWERED THE UNICOM AND SAID THERE WAS LCL TFC AND THEY WERE USING RWY 29 (WINDS WERE GENERALLY FROM THE S). ANOTHER ACFT AND LTT WERE TO FOLLOW US ON THE APCH AND WHEN THEY RECEIVED NO REPLY TO THEIR TFC ADVISORY CALL; I ADVISED THEM OF THE 3 OPPOSITE DIRECTION LIGHT ACFT IN THE PATTERN AND THAT THE WIND DID SLIGHTLY FAVOR RWY 29. I REALIZE THAT THERE ARE NO CLOUD CLRNC REQUIREMENTS IN UNCTLED AIRSPACE AND I AM SURE THIS IS JUST ANOTHER CASE OF BOTH ACFT BEING LEGALLY DEAD RIGHT; HOWEVER; THERE SHOULD HAVE BEEN SOME INTENTION AND POS RADIO CALLS BEING MADE BY THE LCL TFC. PERHAPS WE NEED SOME CLOUD CLRNC REQUIREMENTS AT UNCTLED ARPTS.