As above,
We live in BlackForest,close to Basel and drive back the UK regularly.
Been to Davos this weekend actually… 2:30hs from Basel.
Personally, Chunnel or ferry especially if you can swap drivers.
If ferry then Dunkirk, straight off the boat to the highway and luxemburg. Motorway services for diesel though there is a good 24hr fillip by the port in Dunkirk.
There is a good toll free dual carriageway all the way to St Die, then the tunnel D’ Alsace will be your only payment to get through. This pops you out in Selestat,close to the french Autoroute which is free from there. It flows well and isn’t a boring drive.
Straight down this leads to Basel and the crossing to Switzerland.By the border is a service station, get the vignette here or, actually at the boarder, there is loads of parking.
I would avoid Strasbourg,its always been snarled up with road projects. Colmar is relatively easy too.
French side, careful with speed cameras, Swiss fines are ridiculous,dont speed.
Fill up with diesel in Germany before crossing to Switzerland, shop and booze in Kaufland or similar then take it to Davos.
There is a good Bike Hotel in Davos as well, its close to the COOP which has a cafe in the store for non wallet threatening food. Lookfor Bahntour Davos and translate the page.
If you want to break the journey and stay here, happy to help.