From Alexander Pruss's blog post, edited to only provide mouse support:
To add mouse support, first, go to a game, but don't click the start button.
Then put the following into the URL bar and press enter:
javascript:MAMELoader.extraArgs=(z)=>({extra_mame_args:['-mouse']});AJS.emulate()
(Note that Chrome will not let you past the "javascript:" prefix into the URL bar. You can copy and paste the rest, but you have to type "javascript:" manually.) The game will start, and the mouse will be enabled. You can add other MAME options if you like.
You can also turn this into a bookmarklet by pasting the same line into the URL field of a bookmark.