There has been music with chords and chord diagrams incorporated into it for well over 70 years - as my sheet music collection will testify. True, the chords are a mixture of guitar, uke and banjo - but chords, for all that. The point is that, if it's out of copyright, then you can do what you want. And you can add your own chords to a non-copyright traditional piece.

Just a quick point as well: copyright law in the UK is different from that in the US, with different rules. Also, there is the concept in the UK of "fair dealing", which allows a copy to be made, of a part of a publication, for private and research purposes, for material in copyright.