Switzerland has only been a federal state since 1848. Until the French invasion in 1798 and the resulting "Helvetic Revolution", Switzerland was indeed a union of sovereign states. Most of these states were aristocracies and had very close links to pre-revolutionary France.

As a result of the French invasion in 1798 "The Helvetic Republic" was founded as a centralised state modelled after the French Republic. The centralistic Helvetic Republic was generally not well received by the people, which led to constant civil unrest and civil war, which forced Napoleon in 1803 to give the priviously independent states a lot of their authonomy back.

The first half of the 19th century Swiss politics was then dominated by the conflict between the liberals, who favoured the creation of a federal state, and the conservatives, who wanted to return to the pre-French-Revolution order. This conflict culminated in a brief civil war in 1847, which ended with a liberal victory. As a result the Swiss Confederation was created as a federal state on September 12, 1848. The first constitution of the Swiss Confederation was indeed based on the US constitution (with the notable difference, that instead of a president, they chose to have a council of 7 as head of the executive).

So in short, the answer to your question is: no, the US constitution was not influenced by Switzerland.