You have found a soulmate brotha! I have done this, and the solution is quite nice. Stearns made a one-man kayak that is very small and inflatable. Many stores cleared them out for $49 and I picked up two. They have a capacity in the 250# range (need to check) but I have had a lot of fun with them getting to shoals that a wader can not reach. I also have used them as a caddy / emergency raft on the fast tide areas of Cape Cod with success.
The only dilemma is if you go too small you can't get on it with all the gear it's caddying. Otherwise, the compact one-man inflatable yaks are a very good option for what you're doing.
It weighs around 20# complete with collapsible oars and packs into a bag (included) that is about the size of a large beach bag.
I recommend putting your gear into a fold top watertight bag in the cockpit just in case.
When I am not playing with it the kids love to paddle it around at the beach.
Good luck with your quest.