Including Color Profile in Slices
Hello!
I am working on a kid's book but am running into trouble exporting the pages.
The book is made so that two pages share one illustration and they are exported by slicing them, as the printer needs them seperately.
See below for an example:

Through 'save for web' it looks like this:


However, the save for web does not seem to support me including the color profile with it (it's greyed out, as you can see above here), causing the colors to look darker and less saturated when printed. When using 'export as', I am able to do so, but then the pages aren't sliced. I just want to save them as cmyk images I can throw together into a pdf. Now I read that png doesn't support that and jpeg isn't the best format to use for it and I should use psd or tiff, but they aren't included in the file type list in save for web. Just jpeg, gif, png and wbmp. I did make sure not to tick 'convert to rgb', but it still does not give me the same result as 'export as'.
Is there a way to include the color profile when exporting/saving slices?