For a smaller job, one of these multi-tools will do the casings and they're useful for many other things. There are lots of models, both corded and battery, to choose from. They're a lot cheaper than a dedicated casing saw, too. There are lots of different blades you can get to match the job.
Yup, they work just as well, just quit a bit slower.
If this were my project, all the base would be removed, nails pulled and labeled . Less time and money involved than buying base shoe, priming base shoe, painting base shoe, installing base shoe .