In the inkscape official wiki, there is an extension for exporting PDF files with CMYK color model, but there is no such extension for exporting to EPS.

When saving an EPS file for printing purpose, it is desirable to refer to colors with CMYK. As inkscape originally have equivalent code of CMYK for every color used, it should be easy to save the color codes in CMYK instead of RGB.

Is there a way to export inkscape design to EPS with CMYK color model?

I can say that many people were very happy when that extension was written and made available. A lot of people who use Inkscape, need the CMYK print model. I have no idea why they chose PDF and TIFF for the only output extensions, but I guess PDF is a fairly ubiquitous format. And TIFF well suited for it.

I suppose that if you created a PDF with that extension (with CMYK color), and opened in Inkscape, with the goal of saving as EPS, the CMYK color would be lost.

No, there's no way I know of to save as EPS with CMYK print color model. If you happen to have the skills (and time), perhaps you might want to add that functionality to the existing extension? Otherwise, we'll just have to wait until someone who has the skills, wants to create it.

It might be possible for the OP to import the inkscape svg into scribus (without any loss of vectors) and then export from there into a cmyk eps file. Give it a go and see what happens.