Peterborough Cathedral memorialises her as Katharine Queen of England – and if there's one place to get the spelling of a former queen's name right, it's at her final resting place!
However, Hampton Court Palace, home of Henry VIII, has chosen to refer to her as Katherine of Aragon in all its literature.
The Oxford Dictionary of National Biography writes that this is correct, in line with Katherine being the most popular contemporary spelling, but the Tudors (and therefore the queen herself) may not have spelled it that way. Then, of course, there's the ever-trustworthy Wikipedia... which spells it as Catherine!
Which is accurate?
The first wife of Henry VIII was born in Spain and her birth name was Catalina. Upon travelling to England and marrying into the royal family her name was anglicised, which means that there isn't a definitive historic record.
Also, the notion of 'correct spelling' is modern. For example, Shakespeare's surname has many variants, with evidence that even the playwright himself signed his name in different ways. Consistency with spelling was not a Tudor priority.
With asking her preference out of the question and consensus divided, there's no option but to choose any of the options. Katharine or Katherine or Catherine it is.