If you don't have a Kohler service manual get one. One can be downloaded free from this site or Kohler's website. The cylinder wall should be measure in 6 different areas so you know if there is any tapper in the cylinder. By time you hone the cylinder you will be close to .010 oversize rings which requires a new piston.
K161 motors had 2 different bore sizes. One was 2.875 diameter better known as small bore and the had a 2.938 diameter bore better known as large bore. This was tha same bore size as the K181 motors(8 hp).
Kohler doesn't have a .010 oversize piston. Most will bore the cylinder to 2.938 which is the same as a K181 motor. Another option is checking with Stens. They had a small bore piston.
The crank should be check for out of roundness. Kohler manual wants you to check crank diameter in 6 places. You can have crank journal undersized ..010 if the crank is out of spec. The connecting rod needs replace as Bill suggest. Other items that need replace are governor gear if it is plastic, govnor arm, head bolts, crank seals and gaskets.
Expect to spend $300 to $500 or more to rebuild the motor the right way. The cost will vary on how much you do. I would stay away from the auction sites kits. Their quality isn't that good.
The motor in my 70 is a small bore Kohler K161. It was bored to accept a 2.937 (large bore) piston. I haven't had any problems with it.
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