Notice under the handwheel on the kohler, that there's a raised area with a screw hole in it?
That's the "boss", or "motor boss", what I usually call the motor mount. The distance from the motor mount to the inside of the spoked wheel determines if the crank will fit, and if it clears the handwheel itself (see below).
The other gotcha is that Singer used their own thread, so the screw for a Singer HC likely won't fit the Kohler.
Here's a link to Helen Howes' site, I'm not affiliated with her, but I have dealt with her, and she's great.
http://www.helenhowes-sewingmachines.co.uk/cranks.html
I wonder if HC002 would work for you. Helen may know and she's very friendly.
You'll see that all of the cranks have basically 3 parts:
1. a finger that sits between the spokes
2. the "Crank" - the gear mechanism
3. The mounting bracket.
On the Winselmann I have here, I noticed that the smaller German machines tend to have a long bracket that takes the crank out further than a Singer HC, I think it's because the wheel sits so much lower on the shorter machines, so it needs to come out further to clear.
ETA: That was not a dumb question btw!