Or even better. download a program like VLC and have it write the stream audio directly to a wave file. This keeps it exactly the same as how you heard it. Making it not have to pass through your soundcards opamps and such. Then you have a nice wav file you can edit directly.
On a side note: Being a person myself that runs a music stream. Recording from a stream or "stream ripping" is bad for us independent broadcasters. It costs to us $$ per listener slot. So that slot being taken up by someone that isn't even listening to the stream really is wasting our resources. Some broadcasters have even put in place a limit on the number of hours a client can stream before being disconnected.
But if you do listen and enjoy the stream while recording it, I have no problems with that at all.