Okay, to me this seems like you’re experienced some bug in the wp audio player.. Perhaps consider adding a ticket to wp core if you can’t find any 🙂
Yes that will work but you won’t get any good fallback for older browsers. You can find a good curated list of fallback options here: https://github.com/Modernizr/Modernizr/wiki/HTML5-Cross-Browser-Polyfills#audio
If older browsers are of any concern to you, you basically have to add a fallback 🙂
