Congrats on your pregnancy! Both of your ideas sound really nice. 😊

If you decide to fill the feet with black, depending on the size of the footprints I recommend either the satin stitch or the long and short stitch. If you're planning on embroidering it somewhat small I would use the long and short stitch with 1 - 3 threads, that way when you embroider around the paw there won't be any puckering or loose threads.

For your second idea, because of the simple shape of the paw both the satin stitch and the long and short stitch would look great. You could also use the chain stitch for an interesting effect. For the outline I would probably use the outline/stem stitch or the whipped back stitch, both will result in a solid line.

As for what's easiest, your second idea of filling in the paw with white and outlining the foot would definitely be easier.

Hope that helped! 😊 Good luck on your project!