"Cowan" in the OP refers to the 1865 book Curious Facts in the History of Insects, Including Spiders and Scorpions which states at page
At Hurdenburg, in Sweden, Mr. Hurst tells us the mode of choosing a burgomaster is this: The persons eligible sit around, with their beards upon a table ; a Louse is then put in the middle of the table, and the one, in whose beard this insect first takes cover, is the magistrate for the ensuing year [footnote 1].
Footnote 1 reads: Bayle, iii. 484. Southey's Com. Place Bk., 4th S. p. 439. (316)
There are different editions of Southey's Common Place Book. In the 1850 Southey's Common-Place Book, fourth series at page 454 it is stated:
At Hurdenberg, in Sweden, M. Huet says the mode of choosing a burgomaster is this : the persons eligible sit with their beards upon a table, a louse is put in the middle of the table, and the one in whose beard he takes cover is the magistrate for the ensuing year. — Bayle, vol. 3, p. 484.
Where "Bayle" means Pierre Bayle's 1697 Dictionnaire Historique et Critique
"Huet" is Pierre Daniel Huet
As explained in The Recreative review, or Eccentricities of literature and life, Volume 3 at page 494 and A Handy Book of Curious Information: Comprising Strange Happenings at page 540, Huet travel near Stockholm in 1652 and wrote a Latin poem ""Itinere Sueccio" which explains that in "Hardenberg" the louse custom is used. An English version of the poem is contained in these two references.
A Latin text is contained in Hudibras by Samuel Butler at page 190
Hinc Hardenburgam sera sub nocte venimus
Ridetur veteri nobis mos ductus ab evo
Quippe ubi deligitur revoluto tempore Consul,
Barbati circa mensam statuunter acervam,
Hispidaque apponunt attenti, menta Quirites:
Porrigitur series barbarum, desuper ingens
Bestia, pes mordax, sueta inter crescere sordes,
Barbam adiit, festo huic: gratantur murmure patres,
Atque celebratur subjecta per oppida Consul.
In Memoirs of the life of Peter Daniel Huet, bishop of Avranches at page 124 it says:
We then came to Hardenburg, a town in Overyssel. The reader will probably be amused at the manner of creating the burgomaster of this place, as we learned it from some of the townsmen; and as I formerly gave a narrative of my journey in a copy of verses addressed to John Chapelain, which is published among my poems, I shall copy the lines in which this circumstance is described.
Here the editor refuses to publish Huet's full poet and instead there is the first line "Hinc Hardenbergam sera sub nocte venimus" and the following footnote:
The editor of Huet's work thinks it necessary to say that such a practice never prevailed in this place and that the lines were written either from some idle tradition, or in mere sport
The place was Hardenberg, Netherlands, not anywhere in modern Sweden.
The claim is dubious enough that over 200 years ago an editor felt the need to censor it from Huet's Memoirs