You can ‘black it out’ by placing a smalll black circle on the track above the video and then using track motion to move it so that it covers the offending digit.
(edit) Actually after rethinking it and writing the instructions below you could just place a cookie cutter on a single track of the finger video and cut out the finger to show the black (nothingness) below.
To blur it place exact copies of the clip on two tracks one above the other. Place a blur effect oon the lower track. Place a cookie cutter effect on the upper track and choose circle and size and position it. Using keyframes move the cookie cutter to keep the finger blurred.