You can have your own YouTube Customized Player on any of your websites. Once you customize the player YouTube shows a code which can be copied and embedded on multiple websites.

After the code is embedded on the websites, it does not need any updates. All you have to do is edit your player on YouTube and it will Update the player automatically, not only that but it also shows an updated playlist as and when the edits are made to the YouTube Player on YouTube

Click here to create your own custom player.