archive.org gives the year of recording as 1946 https://archive.org/details/78_shaving-cream_paul-wynn_gbia0001215b The composer and lyricist of the B-side is Benny Bell (Benjamin Samberg).
I would be very happy if someone could contribute some information about this record, especially about the missing label number (instead it says 15984 on the label) or with a picture of the B-side. The record is considered to be the first produced in Germany that has the word "Jazz" on the label. But this is not certain. As you can hear from the recording, the musicians' playing style doesn't have much to do with jazz. Hence the legend that an American military band was playing here, which was stationed in Germany after the First World War.