Originally Posted by
AlienInTheFatherland
Pot luck as far as the Swiss vignette is concerned. Your hire vehicle may already have one, may not. The later on in the calendar year you travel, the more likely it is that it already has one (Switzerland only have annual vignettes).
For Austria, as pointed out above you will also need a different vignette but here you can buy a ten-day one
For Austria, they can be bought at the rest stops upon entering the country and at the start of the stretch of the covered highways. At least when coming in from the North, the West or Southwest.