I'm with you, Lighter. I still think that the word was chosen, over other more specific or contextually appropriate words, mainly because it rhymes with "Dandy" so it fits the rhyme of the lyrics.

I referred to the line from the Red Green Show before on 10 Jan 18 - 09:39 AM, and the word "handy" makes sense in that context. There is probably some intentional double meaning for comedy effect, but essentially it relates to the handyman's skills and knowledge.