I have seen many people out on hikes with inflatables for fishing. What a great way to spend a day! Two options that might work would be the Advanced Elements AdvancedFrame Ultralite Inflatable Kayak & the Kokopelli Packraft Rogue Lite Packraft. The kayak has a bungee lacing that you could use to clip gear to. The Packraft has a larger cockpit with room to put gear inside the raft with you. The kayak weighs 17lbs 8oz and the Packraft weighs just 4lbs.13oz! A third option could also be the Oru Kayak Beach LT Folding Kayak. This one weighs a little bit more at 26lbs, but would eliminate the need for a pump or air filling bag!
Personally, I have only fished from lake shores on extended hikes or backpacking trips. Love the idea of being out on the water though! Happy Trails!