My idea is:
Make this item in illustrator. Give them a specific color name without any conflict with an existing spot color like Pantone or HKS. Define the colors like "Corporate Coor 1" or whatever you want as "Placeholder Colors". Be sure they are defined as global color and spot color. (All spot colors are global anyway.)
In InDesign load the final spot color and in the Ink Manager (it is found on several places, e.g. go to the Swatch panel's menu > Ink Manager) specify the determined spot colors for your "Placeholder colors".
In case of changed colors you need only to choose a different replacement color in the ink manager.
If you need to replace the Placeholder Color with a Process Color, specify a own Spot Color in InDesign with the wanted Color mix, use this as replacement color, but choose the option to output this swatch as process color.
The functionality you describe isn't available in the standard feature set. There may be some scripting solutions to making the replacements when you have to, but here's what I'd do with that to at least save a few steps in the event of an icon change:
Instead of pasting and coloring each icon instance throughout the style guide separately, make a separate, single page InDesign file containing one copy of the icon in each color. Now Place the InDesign file at each icon instance and frame-crop down to the desired color. If/when the icon needs replacing you'll just need to do it once in the linked InDesign file to update throughout.