The verb peddle and the noun peddler are older than your source suggests. Middle English Dictionary gives both pedelare and pedelere in the 14th Century. As spelling began to be regularized we find:
Mr. A. Boyer, The Royal Dictionary, 1728 (a French & English dictionary):
Pedlar or Pedler, S. Un ramonneur ou colporteur, petit mercier ou clincailler, que porte sa boutique sur soi.
To peddle, V. N. Faire le metier de colporteur, de petit mercier, ou de clincaillier
A Dialogue Between Timothy and Philatheus, 1710:
a License to Hawk and Peddle with
Christopher Wase, Dictionarium Minus, 1675 (a Latin & English dictionary):
Agino, are. To peddle; to haggle.
The History of the Life and Acts of ... Edmund Grindal, 1710, records the Archbishop’s Injunctions under “Anno 1571”:
No Peddler, or other, to set his Wares to sell in Church Porch or Churchyard
If peddle is indeed a back-formation from pedlar, it fell together with a homonym spelt both peddle and piddle
D. Fenning, The Royal English Dictionary, 1743:
To PE’DDLE, V. N. [commonly written *piddle] to be busy about trifles.
To PI’DDLE, V. N. [derived by Skinner from pecciolo, Ital. or petit, Fr. Little; and Johnson supposes it comes from peddle, which Skinner says, signifies to deal in small things] to pick at table; to eat squeamishly; to trifle, and attend to small parts rather than the main.
This, too, has a fairly long history:
Guy Miege, The Short French Dictionary, 1701:
to Piddle, pinocher, manger en degouté.
Thomas Durfey, The Marriage-Hater Match’d, 1692.
a good fat Haunch of Venison, boyl’d with Colliflowers, would do well to piddle over.
A sick man that hath a bad stomach, listens after this thing and that thing (he cannot away with all kind of meats) and when he hath what he wished for, he doth but piddle a little at it
William Hinde, The Office and Vse of the Morall Law of God, 1623:
and yet dare you be so bold, as to piddle and picke out something out of his writings
Small wonder that one who does a business in trifles should be conflated with one who busies himself with trifles.