"I want new shoes."
Translation:Dw i eisiau esgidiau newydd.
'Eisiau' is really the noun for 'wanting'. Traditionally the expression 'I want' in Welsh was 'Mae eisiau arna i' = 'There is wanting on me'.
This is quite a cumbersome sentence and in the modern world has changed to follow the normal pattern for simple sentences, but because of its origins the expression doesn't use 'yn'.
There are very few other similar examples of this and so be reassured you need 'yn' or 'n in normal sentences using verbs.