It would be wiser if the Swiss are goaded to attack.
In fact, you can actually declare war, maintain blockade, and do nothing. No drafts, nothing whatsoever, just make sure that no swiss watch can leave their lands, no millionaires can enter their lands, and telephone lines - thus SWIFT - is cut. They have to surrender sooner or later.
Regardless, my point on Monaco and BVI still stands. Monaco, for example, if France cooperates should fall in 1 hour.
Invading the Swiss is about as likely to result in success as invading Afghanistan or Texas. Likewise, trying to goad the Swiss into leaving their mountains is about as likely to result in success as making a Texan leave Texas.
If the Swiss go down the sheer amount of damage they would cause to the EU would far exceed all damage done to Switzerland, even if the damage was so severe as to make Switzerland cease to exist. There's no surprise that the Swiss have recently done military excersizes aimed at defending against French "mobs" (with strong quotation marks). If the EU declared war on Switzerland, a blockade would be possible with the agreement of France, Germany, Austria and Italy (and Liechtenstein, but who cares). A financial blockade would be considerably harder, as the EU would then also have to get the compliance of every major financial center from New York to Tokyo (and good luck convincing London to put its pound to war against Switzerland). It is notable that Russia staved off economic collapse due to sanctions from America and the EU with forex reserves of $385.5B, whilst heavily dependent on oil, whilst oil prices plummeted to record lows. Switzerland's economy is highly diversified, the country can itself be self-dependent, has the largest European gold reserve and forex reserves of $545.4B (one of the largest in the world), and assets all over the world. Excluding any Swiss financial war shenanigans (such as a Swiss-run EU hedge fund using the EU's own money to kill itself), the blockades alone would do horrendous damage to the poor southern and central european countries, and wreck the financial sectors of the western european countries something fierce. Pretty much all of the EU except eastern europe would have many shits to give. In regards to killing communication between Switzerland and the world; keep in mind North Korea can't stop its own citizens using telephones. Switzerland is considerably more connected to the world than North Korea.
The best strategy in my opinion is to first reduce its power, running an extensive propaganda campaign attacking Swiss history while trying to get maybe the French or German Swiss to vote to incorporate themselves into France or Germany (and by extension, the EU). The resulting political turmoil would be negligible for either European country and severe for Switzerland (what with a chunk of it being missing and all) and once Switzerland's capabilities to defend itself are marginalized, pressure it into joining the EU or just ducktape it in enough treaties until it is de facto is an EU province. Invasions of smaller European countries like Monaco is both hilarious and feasible, but not profitable. It can be justified on political grounds, but not economic.