I started my own Radio broadcast but the problem is, the current player just doesn't fit in with the overall design of the website I have embeded it on.

is there a way to use my own custom skin?
I would also prefer to embed it using flash as I assume flash will be supported over more operating systems and browsers (but i don't know flash coding...)

My current website is at: http://www.freewebs.com/uuilliam/index.html

It looks like you are using http://www.wavestreaming.com/ for that audio file. I would suggest going on their boards and asking about ways to customize the audio player. It's all internal flash stuff that wavestreaming makes and provides for you as their service.