Almost all of the History Channel stuff is library. It will likely not be royalty free, it will likely be owned by a major library company. That said you can "Sound Hound" it or a similar app and some of these library songs can be located. Once located you can often find the composer, even ask if he has a chart. As far as playing something like this live no one would care so there should be no issues if you are considering it. If you wanted to rerecord for an album you would need to get permission from the library company. Since they are in the business of making money they would probably let you do it but all libraries have different policies, and there are a few reasons why they may not like it.
Also be aware that music that was around before the library company even existed can be bought up later by a library company and they then own the rights.
The funny thing is that some of that library music is fairly legit. Kosinus, a French company, has collections that feature guys like Angelo Debarre and Marcel Azzola. The tunes are either public domain melodies or fairly generic rip-offs of other well-known tunes, but the playing still sounds good.
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But not sure
Also be aware that music that was around before the library company even existed can be bought up later by a library company and they then own the rights.
www.scoredog.tv
www.scoredog.tv