Given the era it comes from I can't imagine that there's a sexualized meaning to the words. There was certainly bawdy stuff back then, but from what I've read of the era I don't think it was casually thrown around like it is in today's (US) culture.
[1] https://www.npr.org/templates/story/story.php?storyId=497026...
Hold on, let's see what Webster's 1913 says...
2. Skillful in using the hand; dexterous; ready; adroit. "Each is handy in his way." Dryden.
OK, that one seems a bit... vulgar, at worst, and is the sense I took it in, basically.
What I find very funny is sense 4:
4. (Naut.) Easily managed; obedient to the helm; -- said of a vessel.
Might the line have a double-meaning? The obvious one of "knows how to please a woman", but also a near-opposite second reading of "women walk all over him"? Kinda fits with the rest of the song, which reminds me a lot of The Offspring's "Pretty Fly (For a White Guy)".
I have always taken this to mean that if you aren't good to look at, you can still make yourself appealing by being good at things. There is a possible double entendre with foreplay, but I never considered this joke to be suggesting unconsensual groping (I think that's the implication being suggested above?)
https://en.wikipedia.org/wiki/The_Red_Green_Show#Handyman_Co...
[EDIT] yeah, in context it probably just means handling your partner well while dancing as the surface reading, with a possibly-intended somewhat-vulgar "hur hur hur, if you know what I mean" subtext.
I'd never really given much thought to what this line meant but knowing the context it's pretty gross.