If you are looking into globally tweaking shadows, I believe you only have to play with your general lighting setup and exposure settings inside the post process.
Adding a skylight would usually mean ambient lighting and that would do the opposite of what you want which is harsher darker shadows, but depending on how much you want to push the darkness of your shadows ( ex. you need pure black and white like Noir movies or more realistic with slight ambient still in there) you may want to have minimum to no ambient light in there, in all cases i say start with the basics with just one light the sun in this case. Now Unreal’s exposure by default would still give you ambient light even if you don’t have any other light or bounces in the scene, for this reason you have to go to the post process volume and make sure that the exposure settings there under the "eye adaptation max-min settings are the same value, try something high like putting both numbers at 10 and then take the intensity of your sun or light source and push it high to a satisfactory level. you should already be getting harsher darker results with a clear distinction between light and dark areas. make sure your shadows are also high res in the key light (see how to tweak those they are usually under render settings of the light).
later on start adding ambient or more lights as required.
If you are looking into something more stylized i can suggest you look into light vectors similar to the ones they use for toon shading and by creating custom light vectors in the material you can achieve many interesting effects, but it comes with its quirks as well depending of what you want.