No, the person does not know about the date of the event.Please give us some context. Does the person to whom you're speaking know the date of the event? If s/he does, then "which is" is unnecessary in your second sentence (which is otherwise preferable to your first).
Thankyou Keith BradfordIn BE the first one is all right: it suggests that the last three words are an alternative ending. "I have registered for the event, i.e. for 28th February". Otherwise, just omit the comma and use 'on'.
As for the way you've expressed the date: in BE we write on 28(th) February but when we read it aloud we pronounce on the 28th of February.
Thankyou FlorentinaIn that case, with the addition of a comma, your second sentence is still better:
I have registered for the event, which is on February 28th. (BE: 28th February).
If there are several events on different dates, and you are letting the person know which of these you have chosen, then this is better:
I have registered for the event on February 28th / 28th February.