I would be completely honest with the airline or new employer. It shows two big factors about wour character. First, Your integrity. You tell the truth and if you state that you were no longer comfortable with the operation or the airworthyness of the aircraft then any pilot will completely understand. There is no reason to fly something in questionable condition. Secondly, Your judgment as a pilot. You made a desicion and stuck with it. You found a hazard or safety issue and felt it was your duty to refuse to fly a passenger in the aircraft. Both respectable actions.

No airline pilot wants to get into an airplane that is not airworthy. MEL's and differed items are ok because they will be fixed and have been approved for safe opperation. Even if approved you can still make a judgment as the Captain to refuse to fly if you feel it is a safety issue.

I would not be so worried about your situation if you have presented the whole story correctly. Just study and be proficient.

Good Luck