Trimming wood floor boards for running wires under base molding
The tool that is made perfect for this is the type of unit pictured below:



(this picture courtesy of MyToolShed web site)

These oscillating multi-tools can accommodate a variety of blades that permit close cutting exactly like you need to do. Here is an example blade that is what I would use for this cutting job.



(this picture courtesy of Lowe's web site)

These are available from many manufacturers, both AC powered and battery powered. I went for years before getting one just a year or so ago and now use it for many jobs I used to struggle with. A particularly nice feature of the unit pictured is the LED light on the front of the unit to illuminate the cut area.