A replacement to "\mathbbm{1}" with type-1 fonts

The doublestroke package provides blackboard fonts in type 1 format, including the \mathds{1} that you are looking for.

It does not exactly look like those of bbm, but could likely be used as a drop in replacement in your case

Another possibilty is use the package bbold symbol font to get a similar \mathds{1}.

\documentclass{article}
\usepackage{bbold}
\usepackage{mathtools}

\begin{document}
$\mathbb{1}$

\end{document}

Using dsfont you will have:

\documentclass{article}
\usepackage{dsfont}
\begin{document}
$\mathds{1}$
\end{document}