I walleye fish on the kayak all the time from my kayak, it is a lot of fun, and I get to be out on the water. I have used it all, and in it all works, you just have to know when to use it. I have caught them on crankbaits, shadraps, bucktail jigs tipped with worms.
Lately however I have been having the most success with jig and minnow.
And as I have heard it seems to be the way to go for walleye, and for basically every lake that you want to catch walleye on.
Usually pink, white, or half and half pink/white are the most productive color of jig heads. They need to be able to see it if you want them to take the bate.
On rivers jigs work as well, but also I find that crankbaits work a little better in rivers than on lakes.
The main thing to consider regardless of what you are using for lures, is that you get the right depth.
Depth is one of the main problems people run into when they are fishing. No matter if it is walleye or any other type, you need to know the deth of water you are fishing in. That is why I use a fish finder.
Walleye like to sit on the bottom and when we jig we basically drop it till it hits bottom and then take up slack and pull it up an inch or two.
A common technique is to pound the bottom. This is a technique I picked up from a good friend of mine who swore by the technique, and I have to admit it is a good one. When you pound, you baically get their attention. By raising the jig up a foot or two and letting it sink quickly to the bottom to hit and make a thud, then hold it an inch or two off again.
Do this every couple minutes and you will often get a strike as the jig is falling to the bottom or just after you hit the bottom and are raising it that inch or two.
Walleye have good eyesight, and are night time predators with excellent night vision so if you can be out later at dusk or into the night you will likely see more action, same with early morning.
The chances of success tend to die off during midday. While I have had some luck, you can still catch, it's just much harder.
In murky water use bright colors like pink, orange, bright green, white. In clearer water use more natural colors, silver, blues, browns, etc.
Also, be sure you have a nice sensitive rod. Walleye are notorious for having a 'soft' bite and often you will feel them nibble on the minnow a while before they actually take it.
If your rod is not sensitive enough you can often have your minnow stolen and never feel a thing.
I fish a big watersports lake in mine all the time, and during prime ski boat/powerboat/jetski season I just pretend nothing more than 50 feet off the shore exists.
They let any idiot with an ID and credit card rent a boat/jetski these days, so it's just not quite worth the risk to me to fish the islands or channels during the high time of year.
If you do cross big open water, I would recommend a couple of flags/reflectors on poles mounted to your boat so you stick out like a sore thumb.
I know some guys who like to fish for Walleye at night, so make like a Christmas tree if you do that... there are plenty of waterproof LED light strips/bars/spotlights you can rig up that will put out a lot of light without using a lot of juice. And always wear your PFD. Good luck and stay safe out there.