Hi MarcyPB,
welcome to the Affinity Forums!
There are various ways to get rid of the black contour. One would select the pixels, e.g. by color and with an according tolerance (menu Select > Select sample color), and either cut or recolor or fill them with a different color.
Alternatively you could do the entire coloring on a separate layer which gets the color fills based on selections of your scanned image layer below. To hide the black contour then you simply deselect its layer visibility.
MarcyPB got a reaction from Lisbon in Removing ink lines from a scanned illustration