This makes more sense than his. There is more than one person being referred to in the sentence. the word solo is referring to Joe and Daune.
I tried putting his in the sentence and it just doesn't make sense to me. If the sentence was like the following: Joe was not nervous about___his __ solo in the concert then I think it would make more sense to use this word.
Hopefully this helps and good luck. :)
P.S. Don't you mean: Neither Joe nor Daune were nervous about __their __ solo in the concert? Were makes more sense than was.
