I have a few friends who have been doing a lot of kayak fishing for Salmon Sharks here in the waters of AK. It's REALLY caught on the past few years, all over.
It's no joke and something I would not want to do. They said depending on the duration of the fight, they have had the sharks turn back on them and attack the kayak.
No fun when you are only 3 inches out of the water.
Shark fishing out of kayaks has been going on for over 15-20 years on the coast of Texas, especially the lower coast where the drop off from shore is more pronounced. Its not unusual to paddle out to the "short" rigs 3-5 miles offshore to spearfish either.