You can buy it from Van if I recall correctly. You have to connect to Another Wonderful Life on Gamecube first though, to even make him come to the village.
But yeah, the record player isn't all that important if you don't aim for 100% completion.
If you don't have the game to connect with you can always use Gameshark or Codebreaker. Though the songs are nothing new, just remixes/renews of old Harvest Moon music.
It's a real pain in the butt though, since you HAVE to keep connecting and going back and forth between the games while playing them together. It also doesn't help that Van only appears on certain days in the games.