It might help to know what you want to do with these songs. If all you want to do is perform them, then you don't have to worry about copyright, as this is dealt with through fees paid by the venue to the copyright societies, who distribute these as royalties to the composers. The venue pays, not the performer. If you want to publish or record them then it gets more complicated, although this can often be dealt with by a fee to the copyright society rather than having to deal with individual composers.

"Traditional" is not the same as "not in copyright". There are many songs which have become traditional which nevertheless have identifiable composers and are subject to copyright - "Happy Birthday" being the classic example.

If you have specific songs in mind, it might help to tell us what they are.