You can safely fish in the cavern at the end of the water tunnels. Nothing saw invis, so I had no problems getting my alt druid in there. There are a few mobs in the cavern, but they're far enough away from the water that you can fish without getting aggro.
At 200 fishing I'm getting the Blowfish Barbs about 20% of the time.
Sadly, you cannot bind at the fishing spot.
Happy Fishing !