As egreg says, it can't be done in a generalized way. And in this answer, I don't have merriweather font, so I just demonstrate the technique (and exaggerate the effect) on the standard CM font.
One can locally achieve what you ask by making - active; however, that breaks many, many things, because it means the negative sign has been redefined. So the compromise I propose here is a macro pair \newhyphenON and \newhyphenOFF. In this way, you can turn \newhyphenON when you are just typing text with your shifted hyphens, and turn it off for just about everything else.
In this MWE, I show how, when \nehyphenOFF has been invoked, the minus sign is restored for use in a \raisebox. But when \nehyphenON is invoked, the shifted hyphen is in place.
\documentclass{article}
\usepackage[T1]{fontenc}
%\usepackage{merriweather}
\sffamily
\begin{document}
\let\svhyphen-
\def\newhyphen{\raisebox{-.5ex}{\svhyphen}}
\catcode`-\active
\def\newhyphenON{\catcode`-\active\def-{\newhyphen}}
\def\newhyphenOFF{\catcode`-=12\let-\svhyphen}
\catcode`-=12
\newhyphenON
h-y-p-h-e-n
\newhyphenOFF
h-y-p-h-e-n X\raisebox{-1ex}{X}
\newhyphenON
h-y-p-h-e-n
\newhyphenOFF
h-y-p-h-e-n
\end{document}
pdflatexthe only possibility is to modify the font, I'm afraid. – egreg Jan 17 '14 at 20:18fontinstwhich provides commands enabling you to control this. Note that it already depends on virtual fonts. There's no reason not to create a distinct set for your own purposes but I'm not clear whether the existing virtual fonts include any tweaks which you might lose out on. (There doesn't seem to be a script or Makefile provided as source, at least in TeX Live. This might mean the commands were run directly without any tweaks - or they were added manually.) – cfr Jan 17 '14 at 22:08