If the stucco is the real 1940s stucco, which there is no reason to think it is the modern day equivalent of what is considered stucco, the trim will be imbedded, or so it should be.
The only issue with what I see in the picture, and a closeup would be needed to confirm, is how the side trim meets the sill. The side trim should not be overhanging the sill. It suggests the side trim was added later, but it was done a lonnnnng time ago from what the paint layers look like. Even if it was added after the stucco was done you will be contending with the line left over from the edge where the trim used to be, unless you replace the trim with the same width piece or wider.
The problem will be if you are replacing all the window trim around the house. There will be flashing at the top of the window that will quite compromised if the trim is taken out from under it. If it is just the window or windows on the porch where the rain will never hit the top, the flashing or lack of it will be no concern.