tcolorbox breaks the verbatim definition of ltugboat documentclass

The [\small] is a feature of ltugboat verbatim. If you use a different verbatim, you have to get rid of it. At least, I can't picture a different solution, sorry.

Instead, you can use something like

{\small \begin{verbatim}
...
\end{verbatim}
}

But I would guess you already knew that.

I don't know how much tcolorbox relies on verbatim as defined by the homonym package that it loads, so something like

\documentclass{ltugboat}

\let\ltverbatim\verbatim
\let\ltendverbatim\endverbatim

\usepackage{tcolorbox}

\let\verbatim\ltverbatim
\let\endverbatim\ltendverbatim

may possibly yield problems when embedding verbatim material in tcolorbox environments.

A different approach is to use fancyvrb for your verbatim (non tcolorbox) material:

\documentclass{ltugboat}

\usepackage{tcolorbox}
\usepackage{fancyvrb}

\usepackage{lipsum}

\begin{document}

\lipsum*[2]
\begin{Verbatim}[fontsize=\small]
\documentclass{article}
\usepackage{tikzduck}
\begin{document}
  \begin{tikzpicture}
    \duck
  \end{tikzpicture}
\end{document}
\end{Verbatim}
\lipsum[3-5]

\end{document}

(avoid indenting verbatim). You can also set \small size by default with \fvset{fontsize=\small} in the preamble.