How to export different color profiles when defining color in Paragraph and Object Styles?

My team produces a monthly publication using branded colors (The brand colors were chosen by others and cannot be changed or updated). The colors are defined in several profiles: Pantone Coated, Pantone Uncoated, CMYK, and RGB. When I took this job I created a indt template file that has all the CMYK colors added as swatches and have all objects and text colors set using Object and Paragraph styles from those CMYK based swatches.

We recently changed the paper that our printer uses for the publication but the CMYK colors are not reproduced accurately on this paper. Is there a way to export two versions, one for each CMYK and Pantone Spot color without having to have two versions with the Styles changed? Is there a way to automate this process?