"The mouse was disappointed that it did not find cheese."
Translation:De muis was teleurgesteld dat hij geen kaas heeft gevonden.
It's 'de muis', therefore it is referred as 'hij' or 'zij'. If it was a het woord, it would be referred as 'het' (but that excludes living things, because we would refer to their actual gender, so 'het muisje' would still be 'hij' or 'zij').
When referring, it is important to know the gender of the word itself. Neuter words are easy to recognise, since they all use 'het'. Masculine and feminine are a bit difficult, since they both use 'de'. In the Netherlands we often don't know what gender a word has, so we treat all de woorden the same: masculine. However, in the more southern parts of the Netherlands, and in Belgium, people often do know whether a word is masculine or feminine, and will know to refer a word as 'hij' or 'zij'.
De woorden can be either 'hij' or 'ze', depending if it is a masculine or feminine word. In the Netherlands we normally don't make the destinction anymore, and use 'hij' for all de woorden (unless it is obvious it's feminine, like 'vrouw' or 'lerares'). Even so, the sentence is wrong, because, like you said, you have to use 'geen'. If there was an article in front of 'kaas', then you have to use 'niet': De muis was teleurgesteld dat hij/zij/ze de kaas niet vond. :)
(I looked it up in the dictionary, 'muis' is feminine :D )