Yeah, it looks like it's not a standard mini-usb cable. I just said that because the only other device I have that uses USB, also uses the same cable (my NetMD minidisc player). Maybe go to RadioShack and ask them if they have a cable. Though it'll be longer than you probably want.
And yes, you'll be able to connect it to other computers. Just make sure you get a cable that has one end that's normal and one end that fits the mp3 player.