How to disable links completely using hyperref package?

Thanks to @egreg, the recipe is

\usepackage[options]{nohyperref}  % This makes hyperref commands do nothing without errors
\usepackage{url}  % This makes \url work

Add the draft option to your \hypersetup:

\hypersetup{draft}

or as you already mentioned:

\usepackage[draft]{hyperref}

hyperref itself provides the NoHyper environment:

\documentclass{article}
\usepackage{hyperref}

\begin{document}
\begin{NoHyper}
...
\end{NoHyper}
\end{document}

This still creates bookmarks (listed in the "Bookmarks" navigation panel of PDF viewers). If these shall be suppressed too, add option bookmarks=false:

\documentclass{article}
\usepackage[bookmarks=false]{hyperref}

\begin{document}
\begin{NoHyper}
...
\end{NoHyper}
\end{document}