"Touch up", in America, usually means "correct the remaining or accumulated minor flaws in". It is often used, e.g., with regard to inspecting a paint job and dabbing the odd spot that you missed or mussed, or rereading a MS for omitted words & infelicities of style. I doubt if the phrase means quite that in the song, tho %^).

I agree with some of the contributors to this thread in liking the song the way Mr Hicks wrote it. Even on the printed page, it comes thru with the voice of a man who recognizes that he has some of the traditionally masculine vices & that his womenfolk have some of the traditionally feminine virtues. So what? That's not all there is to life, but it's part of the truth.