How to block the package mathptm locally?

Question

I declare the package mathptmx in the preamble, but I want to use \mathcal for the letter I without mathptm:

The symbol omega is prettier with mathptm but \mathcal{I} is not.

\documentclass[12pt]{article}
\usepackage{amssymb,amsmath}
\usepackage{mathptm}
\begin{document}
$$\mathcal{\omega}$$
$$\mathcal{I}$$
\end{document}