The rules on copyright depend on which legal jurisdiction you are in. In many jurisdictions, including the US, copyright arises automatically whne the work is created. It does not have to be formally registered, although doing so may help support a claim, and may be necessary before a legal claim can be brought for breach.

If you are making a CD you will need a mechanical copyright licence. Where the composer is a member of a rights organisation eg Harry Fox then the agency will issue the licence on their behalf. However if it not registered with the agency this does not mean it is not copyright, instead it means you must negotiate with the rights holder yourself. The difficulty then, as you are finding, is identifying who this is and how to contact them. If the original composer has died the rights may belong to their estate, but they might have been assigned to a publisher.

If you cannot trace them, you will need to decide whether to go ahead without permission. You will need to consider how big a risk this might be. Do you think it is likely that the rights holder will object if they later find out, and if they do are they likely to be satisfied with a royalty payment? I have found that most people in the folk world are generous and are often willing to waive royalties, which in any event are unlikely to be much. However you can never be sure, especially when the rights have passed to someone else who may be protective of them. It may help if you can show you had made every effort to find the rights holder. Only you can decide whether or not to take the risk of going ahead without permission.

You also need to consider the lyrics, which may also be copyright. The lyrics are by Hiram Cody, who died in 1948. Copyright usually runs for 70 years from death so they are probably now in the public domain. But check for yourself.

There is plenty of information on mechanical copyright on the internet and if you are making a CD you do need to understand this. However remember that the rights agencies are concerned only with protecting the rights of their members and don't cover all situations.