I'm not sure why they would be different, unless the 63 Dart's are different than the 63 Valiant's. I put a heater box out of a 63 Valiant in my 64 Valiant and the heater core was the same all the way up to 69.
[Click image for part details] CR9104
Heater core for all 1963-1969 A-body models.
$65.00
This is at Year one.
Lee