Except that Touchstone was Armin's, not Kemp's, character, and you mean Will Kempe. You have to look at the pieces in the period 1592-1599 to find anything which might contain his work: Comedy of Errors, Love's Labours Lost (and Won, which is lost), Romeo and Juliet, and Much Ado (where Dogberry's lines are overtly marked as his in the Folio edition). Which pretty much brings us down to Much Ado, which was only staged after Kempe had been forced out: Kempe was a dancer, and possibly a tunesmith, if the Jig was his, not a songsmith.
'Twas A Lover, which has this Nonnying about, comes from As You Like It, work on which began no earlier than late 1598, by which time Kempe had overplayed his hand in becoming a shareholder in the Company and was on his way out, and was finished probably before Armin joined in 1600. It was written by Thomas Morley, who published it in his First Book of Ayres of that year.
I'll spare you my work proving that Shakespeare left gaps in his text for these specialist pieces, much in the same way pantomime does for it's stars' hits of the day these days. The point is that this is legally documented as Morley's work, not Shakespeare's, not Kempe's, and therefore belongs in the heritage of Italianate madrigalia, and not English folk, even of those days. I attribute Touchstone to Armin as it has distinctive touches of his new English Humour: the role was probably worked up by him in the years which followed. The first sign of Armin in the Company is 1602, and he's only seen as being properly installed in 1605. However, there is a strong case that the finished works were the output of much fine-tuning, and may not have been what was first performed, let alone written. We all know the finished product gets adapted in rehearsal...