My diocese's confirmation planner says this:

"No music is necessary during the anointing with Chrism. However, subdued instrumental music may be played when there is a large number of people being confirmed. There should not be choral or congregational singing during this time."

While it's clear this isn't authoritative outside my diocese, I'd imagine this came from a reputable source, as my bishop is the last one to make up things in the liturgical sphere. Maybe someone can back this up with an actual document?

In addition to that, no, you probably won't have any time to sing anything if there's only 4 or 5 confirmandi. The anointing will probably be done in 30 - 50 seconds. No time at all really.

I have not seen the official directive from my diocese, but have been told that it is forbidden.