Help settle a fight!

A friend of mine, who is not pregnant, but hopes to be soon, is having a name dilemma. She would like to name her first daughter [name_f]Catherine[/name_f] and call her [name_f]Kate[/name_f]. She very much prefers the “C” spelling of [name_f]Catherine[/name_f] and the “K” spelling of [name_f]Kate[/name_f] but doesn’t think she should switch the first initial for the nickname. So either she’s stuck using [name_f]Katherine[/name_f] to get to [name_f]Kate[/name_f], or she’ll have [name_f]Catherine[/name_f] and have to spell the nickname [name_f]Cate[/name_f]. I keep telling her that she’s making a problem out of nothing, that [name_f]Catherine[/name_f] with a C can be nicknamed [name_f]Kate[/name_f] with a K and have pointed out several people who have done that ([name_f]Kate[/name_f] Middleton!). So do you agree with my friend that it would lead to misspellings and be confusing? Or do you agree with me that this is a non-problem?