Is there a Media player that can skip the silent parts of an audio/video?

I think that the closest you will get is to use a Media player that shows the waveform of the track you are playing. If this is something you would consider it would be worth looking at foobar2000 as it shows the waveform of the file allowing you to see where the "silent" parts are!

You will need to install the Waveform Seekbar component in addition to the main foobar2000 software to achieve this, the software is incredibly lightweight and i have used before for a similar situation a few years back!

Use Chrome with the open source extension Skip Silence.

Note that additional steps may be necessary if you are trying to play a local file.

Here is the GitHub repository for this extension.

Tip: If you don't like to install too many extensions that may affect your browser's performance, you can always create a new profile/user which will allow a separate profile of extensions to be enabled.