I wouldn't worry too much, I had rather odd songs sung to me, Hawaiian War Chants, the Aggie War Chant(strictly football), etc, and I survived nicely.

One old one my grandmother sang often was By By Low, I know I used that often for my girls. Folk music works nicely. Many of the Jewish folk songs I remember hearing were very gentle, although I have no idea what was being said, they sounded gentle.