Welcome Alpoh!

The LW media player is often the subject of complaints here; I don't know of anyone who would recommend using it.

Windows Media Player has the option to shrink to the bar, and surely there are many other free players that will do just what you want. I recommend searching majorgeeks, download, or tucows (all are .com).
I often use a simple little player called 1by1 that you might like; find it free @ above sites.

I don't expect LW developers to put much, if any, effort into improving the player.