Indeed you can, with the apk file you may change the extension of the file name from 'apk' to 'zip'. Example is changing zesh-mod.apk to zesh-mod.zip. This will turn the format into a zip archive where you can extract the content, mainly the assets folder. Within the 'assets' folder, there should be an 'index.html' or similar HTML document. Now, depending on the way the mod was compiled, that could be the finished HTML, and thus you only need that HTML, or it may require the other assets within that folder such as the 'mygame' folder. I would recommend extracting the modded game turned zip archive to some directory, and select 'index.html' to be opened in one of your browsers. Browsers, like Firefox, should automatically save your progress if you ever decide to close the game and reopen later.
Unfortunately, I am unfamiliar with how to extract the playable data from an exe file so that you may use them on a browser.