If I travel to Ghana and marry him there, will that have any effect with immigration here in the United States?

Upon marriage abroad, the approved K1 fiance visa will become moot, but you should be able to commence consular processing to achieve your goal of enabling him to come to the U.S. and become a Lawful Permanent Resident. It would be wise for you and your fiance? to consult with an immigration attorney who, upon learning all of the relevant information about you and your fiance?, will be able to advise about eligibilities, options and strategies and would be able to offer legal representation in the often complex application process.