I realised that the Finnish Wikipedia page for Kuksa has (unsurprisingly really) more information that the English page and says this about how they are finished:
"Tekovaiheessa aitoa kuksaa keitetään suolavedessä, jolloin suola imeytyy puuhun. Suola liukenee myös kuksasta juotavaan juomaan, jos kuksaa ei ennen käyttöönottoa käsitellä.[1] Suola on hygroskooppista ja sitoessaan kosteuttaa estää puun kuivumisen ja halkeamisen. Suolan liukenemisen voi estää käsittelemällä sisäpinnan kahvirasvalla, mikä tapahtuu kaatamalla kuppiin kahvia, joka muutaman minuutin päästä kaadetaan pois, sekä hinkkaamalla sisäpintaa käytetyillä, märillä kahvinporoilla. Tällöin kahvirasva imeytyy kupin sisäpintaan ja muodostaa siihen kalvon, joka estää kuksan kuivumisen ja halkeamisen ja vieraiden makujen imeytymisen.[1] Jotkin teollisesti valmistut kuksat käsitellään parafiiniöljyllä.[1]
Kuksan makua voi myös muuttaa tilkalla viinaa ennen rasvakäsittelyä.[1]"
Google translate gives this:
"In the making stage, genuine kale is boiled in brine, whereupon the salt is absorbed into the wood. The salt is also soluble in the drink from the kuka, if the kuga is not treated before being put into service [1]. The salt is hygroscopic and when bound, moisturizes to prevent the wood from drying out and cracking. Salt dissolution can be prevented by treating the inside surface with coffee fat, which is done by pouring coffee into the cup, which will be poured out after a few minutes, and by scrubbing the inside surface with the used wet coffee grounds. In this case, the coffee fat is absorbed into the inner surface of the cup and forms a film on it, which prevents the drying and cracking of the kicks and the absorption of foreign flavors. [1] Some industrially manufactured kuksas are treated with paraffin oil. [1]
Kuka flavor can also be changed with a drop of liquor before fat treatment. [1]"
There's some definite translation mistakes (there is no mention of "genuine kale" in the original text so who knows where that came from) but as far as I ca see, they would boil them in salt water then pour coffee into the cup, leave it for a few minutes then rub in coffee grounds ("coffee fat"). I should of guessed coffee was going to be part of the process
I might give this a try. I only have crappy instant coffee (left over for guests; neither me or the SO are into coffee) but it should do.