"Don't know"s are necessarily problematic here. If "Don't know" was explicitly presented as an intermediate category in the questionnaire, there is a case for treating it that way.
That would be, in my experience, highly unusual; and it doesn't appear to have been the case here.
I'd argue that the only defensible actions otherwise are
to regard "Don't know"s as missing and to exclude them from the model fitting
to retreat to a multinomial model that doesn't regard the response or outcome as ordinal (but don't be surprised if the "don't know"s don't fit easily into any model).
(I'd assert that "categorical" (wide sense) as including ordinal is more common in statistically flavoured literature than "categorical" (very narrow sense) as meaning nominal only. It is, I think, uncontroversial to underline that narrow and wide senses are both encountered.)