How do I open the body of K-10430 apart to replace the valve cartridge kit that's leaking

You need patience/care to open up the faucet and replace the parts.

See if you can understand the diagram on page 15 of the installation guide. The link to the guide is:
http://www.us.kohler.com/webassets/kpna/catalog/pdf/en/1084448_2.pdf

try cleaning the inside of the valve with 1500 grit wet sandpaper. and then put a lot of waterproof plumbing grease in there and also on the cartridge. sometimes you can get a build up of hard water inside the valve body and that will cause leaks. just dont over do it with the sandpaper and dont anything more abrasive than 1500 grit.

If you faucet is leaking, try this simple step to see if it will stop. First, turn the water supply line off under the sink. Next, open the valve that is leaking all the way open. Take a wrench and tighten the nut just below the faucet handle. Now turn the vale to off and open your supply line and then test the faucet again. What you are doing here is tightning the packing nut inside the faucet. Good luck.

The A-S single lever kitch faucet is terrible. If it is the one I think it is, then it has three screws that mount the cartridge down into the faucet body.If these are not torqued perfectly evenly, the faucet leaks. I suggest getting a Moen to replace it.

These faucets can leak in three different places:

1. Internally at the valve seat
   You'll see water dripping from the spout. This means the rubber washer is worn or damaged. To replace the washer, remove the decorative cap from the handle. Remove the retaining screw and pull off the handle. Remove the decorative cover, called an escutcheon, if there is one. Unscrew the packing nut counterclockwise. Unscrew the valve stem and remove it. Remove the screw that holds the rubber washer in place. Because these washers come in many shapes and sizes, you'll want to take the old one to the hardware store and buy an exact replacement. Be sure to buy two washers so you'll have one for the other valve. Replace the washer and reassemble the faucet.
   
2. Around the handle
   If you see water coming from below the handle, the packing nut is leaking. Older faucets have a string-like graphite packing material wrapped around the stem. Newer faucets use an O-ring. First try tightening the packing nut clockwise... about one-half turn. If this doesn't stop the leak, remove the packing nut and replace the packing or O-ring; then reassemble the faucet. If the valve is using the graphite packing material, it might be a clue that you should shop for a new faucet.
   
   
3. Between a pivoting spout and the body
   The spout might be held in place with a packing nut, similar to the faucet stem, or it might have a nut at the top of the spout. In either case, remove the spout and replace the packing material or the O-ring seal. Then reassemble the faucet.

Single lever faucets also are known as "washerless" faucets. They are easier to repair than compression faucets after you determine what type of faucet you have. There are three types of washerless faucets: ball, ceramic disk and cartridge.
Leaks are evident in two places... dripping from the spout and seeping from around the spout where it joins the body of the faucet.
Leaks from the spout indicate that the ball, disk or cartridge is leaking. To repair, turn off the water to the faucet, then remove the handle. The handles on ball-type faucets are held in place with a setscrew that requires an Allen wrench to loosen. Ceramic disk and cartridge-type handles usually are held in place by a screw hidden beneath a cap.
On ball and ceramic disk-type faucets, remove the ball or disk and replace the seals. You can buy replacement kits for these faucets at the hardware store or home center.
On cartridge-type faucets, remove the spout and pull out the retainer clip that holds the cartridge in place. To remove the cartridge, pull on the cartridge stem with a twisting motion. If it resists, install the handle so you can a better grip on the cartridge to pull it out. Take the cartridge to the hardware store or home center and purchase an exact replacement kit.
Reassemble the faucet according to directions.
Leaks at the spout-to-body joint indicate an O-ring failure. Disassemble the faucet as described above. Remove the spout sleeve and replace the O-rings. It's a good idea to replace these seals if you have the faucet disassembled for repair of the ball, disk or cartridge.

After removing the oval button cap on the back of the handle loosen the set screw behind it and pull the handle up. The bonnet is threaded so hold the faucet body with one hand (I used a gel hot pad for a better grip) and turn the bonnet counterclockwise. Be careful not to let the entire faucet body turn or it may loosen the bottom bolt that keeps it pulled down onto the base o-ring. Then remove the nut in the same manner and you can simply pull the valve body straight up. To install just reverse this procedure.

Under the handle, there is a curved trim ring at the top that needs to be unscrewed from the base. This can be on tight due to hard water buildup. I cut two strips of rubber to wrap, one to wrap around the trim ring and the other to wrap base while using channel locks for the trim ring and a pipe wrench to keep the base from turning.

After that is off, you will see a large hex head retainer nut that holds the valve assembly in place. A spanner wrench will get that off fairly easy.

Reassembly is the reverse. Kohler specs the hex nut to be torqued at 9 ft-lbs or 1//4 turn past hand tight.

Kohler gives replacement cartridges for this problem

The single handled faucets have a valve cartridge which needs to be replaced when it leaks. Disassemble the handle to find the valve inside. Take the valve to the hardware store to be sure you get the right one and reassemble. To disassemble, pop the cap off the lever, unscrew the single screw, then use slip-joint pliers to loosen the retainer nut. lift the cartridge out with pliers taking note of the direction of the notch at the top of the stem. Be sure to reassemble with the notch facing in the same direction. You should replace and lubricate the O-rings when you change the valve cartridge.
Since you have the numbers for that particular faucet, you might want to call around to find the cartridge first. Different models have different valves, so be sure yours is correct.

Actually one or more o rings in your faucet are worn and leaking. get a faucet repair kit especially for your k-10430 if you are mechanically minded. If not call an appliance store and see how much they would charge to install a repair kit. regards, joe

ps kindly rate my answer as helpful as this is the only credit I can get for assisting you. ty.