I have a Perception America (circa 2000, 13'4") which was my first kayak, and was purchased for the main purpose of fishing out of it, but I knew I'd want to do a little exploring with it, too. It is 27" wide, and has a huge cockpit. It's great for fishing, but kind of on the doggy side as far as forward moving efficiency.
I also have a John Winters designed QCC400X (15'3", 24" wide)that I use for day tripping, and it is an extremely efficient hull design.
John Winters also designed a boat called the Tasman Sea, which is 13'6" long and 25" wide, and I've always thought that would make a better fishing boat than my Perception America, because I know it would be a more efficient hull, and therefore paddle easier (if you're unsure about that claim, Google up "John Winters kayak" or look at the QCC website to find links about him. He designs very efficient hulls.
Anyway, the Tasman sea would be a good, fast, stable, short kayak very suitable for fishing with one modification. That is, make a longer cockpit opening so you have room to put a tackle box in front of you, among other things, and be able to reach it (them).