Short answer: No. Holland is not a nickname for Switzerland. The two are entirely different countries.
The mix-up likely stems from the similar-sounding names or a vague association with "neutral European countries." However, Holland specifically refers to the two western coastal provinces of the Netherlands—North Holland and South Holland—which became the economic and political heart of the Dutch Republic and later the Kingdom of the Netherlands. Today, "Holland" is often used informally (though imprecisely) to mean the entire country of the Netherlands.
Switzerland (Swiss Confederation, or Confoederatio Helvetica—hence the abbreviation CH) is a landlocked Alpine nation in Central Europe. Its historical nickname is the Helvetic Confederation, derived from the Helvetii, a Celtic tribe that inhabited the region in antiquity.
So, while both are prosperous, stable European nations, they are distinct entities with no naming relationship.