Please do sing them!! It is entirely appropriate. And yes, when there are sensitivities because of language or terms used then, as opposed to now, take the time to explain - but these songs and stories should be heard!!

As for Civil War vs War Between the States - us southerners can get riled over the term Civil War, but that is a modern aversion. If you read correspondence or hear quotes from Robert E, Lee or Stonewall Jackson or Jeb Stewart or Nathan Bedford Forrest or virtually ANY of the great southern Generals from they period, the term was Civil War.