Checked with your regular vet? They usually know who’s open when in their area. And there’s probably one on call if needed you might be able to arrange to get them done with.
Sort of a bad choice of day to be leaving though.
2 January is not a holiday in canton SZ - so you might try Marigin, in Feusisberg SZ (left side of the lake and up a bit).
I’m not sure if they are open on the 2nd, but tomorrow is a normal working day, so call to see if you can schedule the treatment for the 2 Jan.
You could also try most vets in SZ.
Just saw your last post - do you have a car? You’ll need one to get to Marigin. How far can you travel? And, do you speak German (most of the vets at Marigin speak English, but the telephone staff might not.)
If you don’t have a car, you might try Frau Staub in Einsiedeln, her practice is walkable from the train:
https://www.tierarztstaub.ch
Or Vets4Pets in Lachen:
https://www.vet4pet.ch
Or Frau Rusch in Wilenbei Wollerau - a bit of a hike from the train, though.
http://www.tierarzt-wollerau.ch/index.html