You are not alone.  This particular set of the song was noted by H.E.D. Hammond from John Hallett of Mosterton, Dorset, in 1906.  The Watersons have changed it a little, doubling the length of the chorus and omitting one verse.  Instead of Clean up to his harness, for example, Mr Hallett sang Right close up to his arse-O.  The missing verse was:

If ever I should meet with the old shepherd's wife-O
I'll make him a cuckold all the days of his life-O!

In the light of that, it should be even more obvious what the narrator intends to do to the shepherd's daughter.

So far as the word Twankydillo is concerned, nobody really knows what it meant.  Frank Purslow (The Constant Lovers, EFDSS 1972) remarked:

"The origin of the word "Twankydillo" has never been satisfactorily explained, although in the usual "Blacksmith" versions it has been suggested that it might represent the sound of the hammer on the anvil (in a literal sense!).  Personally I doubt this very much.  For one thing there is no evidence that the "Blacksmith" versions are older than the other bawdy verses in existence; my own personal opinion is that the opposite is the case.  For an explanation of the word I suggest that a good clue lies in the phrase (common to all versions) and he play'd on his merry bagpipe(s)..."