On second look, your suggestion is a jewel. It is grammatically ambiguous, but both interpretations have the same meaning. 

The {-meH} clause can apply to either the object or the main verb. Either you know the ship building method, or, for the purpose of building a ship, you know a method. 

Beautiful. 

It's really just the standard way of recasting a so-called "question as object." Find a way to translate the English part with the relative pronoun into a Klingon noun phrase. I'm not going to take credit for anything special here.

ta'lIj meq vISov I know why you did that
SeSamIy taw pawmeH mIw qaja'laH I can tell you how to get to Sesame Street
Qang Hegh poH vISov I know when the chancellor died
DaqlIj vISov I know where you are
Qu'lIj vISov I know what your job is

-- 
SuStel
http://trimboli.name