From around the time of the compiling of the Westminster Confession of Faith [1643-46] there is abundant evidence to be gleaned that the term 'psalm' in the chapter 21 section 5 is not referring exclusively to the Psalter. This section of the Confession reads:
The reading of the Scriptures with godly fear; the sound preaching and conscionable hearing of the Word, in obedience unto God, with understanding, faith, and reverence; singing of psalms with grace in the heart; as also, the due administration and worthy receiving of the sacraments instituted by Christ; are all parts of the ordinary religious worship of God: beside religious oaths, vows, solemn fastings, and thanksgivings, upon special occasions, which are, in their several times and seasons, to be used in a holy and religious manner.
The men who compiled these worthy documents of the Westminster Standards could not be shoehorned into the exclusive psalmist camp.