Switzerland never was cool when it came to invasion. The three times the Swiss army has been mobilized every single one of the possible invaders had multiple numerical advantage, as well as a technical advantage. The only chance Switzerland had in case of being attacked was to use the terrain to their advantage and making use of fortifications.

That being said; the quote "Shot twice and go home" is most likely nothing more than a nice story that never actually happened. And what do you mean with the "the whole 'give no quarter' that the Swiss have used over the years"? Switzerland is enormously proud of their humanitarian tradition, giving no quarter would be a harsh violation.