I don't think this is a feature of Lightroom.
Since true shadows tend to be somewhat desaturated of color anyway, the effect of doing this would be hard to see, which may be one reason there may be no clear path to doing it in LR.
I see and you probably saw as well a way to increase shadow color saturation in Develop module's Split Toning (change Highlights to Shadows and add Saturation--but the Saturation default there is 0 and won't slide negative). Note also this feature interprets shadows at medium gray, not dark gray.
Are you getting color noise (grain with odd colors) in the shadows that you want to desaturate? Then you could try Develop > Detail > Noise Reduction, click the small crosshair icon in Detail and use it to sample a shadow in your image, then slide Color towards 0. The effect is subtle though; you may be looking for more impact. Less desirably maybe Develop > HSL / Color / B&W > click on the word Color there, select the Color that comes closest to the one (if there is only one) you want to desaturate and move Saturation there to the left could do what you want, but of course this will reduce that color throughout your image, not just in the shadows.
Per Berntsen's idea sounds promising and worth a try too.
You could use the adjustment brush with saturation set to a negative value.
But he said he didn't want to brush.
Yes I see that now, but I'm not sure if there's any other way to do it.
Maybe something could be done with the Color panel, provided the unwanted color is only found in the shadows and nowhere else in the image.
Not Lightroom- I know, I know, I know- this is a Lightroom forum!! but Photoshop can do this exactly as you want. If you have Photoshop!
1. Copy background layer [Ctrl+J]
2. Apply "threshold" to copied layer [Image>Adjustments>Threshold]
3. Adjust threshold to select shadow areas. Invert this layer [Ctrl+I ]
4. Copy the threshold layer- [Ctrl+A ] [Ctrl+C ]
5. Select background image layer and Add a Saturation adjustment layer.
6. Select the Mask on the adjustment layer [ALT + LClick ]
7. Paste the threshold layer into the mask on the Adjustment layer [Ctrl+V ]
8. Click Saturation layer Icon and Adjust Saturation on the adjustment layer.
9. Delete the 'Threshold' layer. (it was only needed to create the mask)
10. Save image and back to Lightroom.
Can you post a link to a shot that has the effect you want to achieve?
I have the same question. This is 2 clicks in many film color grading software like DaVinci Resolve. And it is a common technique that is needed to allow more dramatic adjustments of color while preventing color adjustments from making shadows feel cartoonish. We need this in LR and Premiere's lumetri color.