I would do something like the following (partially motivated by what Roman suggested): make your LaTeX file be
\documentclass{article}
\begin{document}
\input{scriptoutput.tex}
\end{document}
and generate the file scriptoutput.tex
using
/usr/local/bin/my-shell-script.sh > scriptoutput.tex
You could encode this in a makefile if you want to have it run automatically when necessary. Alternatively, you could use the TeX \write18 command,
\documentclass{article}
\immediate\write18{/usr/local/bin/my-shell-script.sh > scriptoutput.tex}
\begin{document}
\input{scriptoutput.tex}
\end{document}
and I think that would automatically run the shell script each time you compile the document. The \immediate
is necessary to ensure that the script is run when LaTeX encounters the command, rather than waiting until a page of output is written. (See this question for more on the shipout routine.)