Change type of mapping field without reindex?

No, you cannot update mapping for the existing fields without re-indexing.

though, why don't you use the current date.date sub-field instead?

also you might think of adding a new field like date_new for example. however, this will also only works for newly indexed documents, not the previously indexed ones.

you might find much similar questions as yours, here and on the Stackoverflow (e.g. below one)