First, you must get a tax expert in Switzerland for your Swiss funds. Also contact a knowlegeable professional (CPA, Lawyer, etc) in the city where you intend to be residing. I can't advise you on that aspect. We (a client and I) use one in Zurich and another in a different town on the French side of the country. You should know that once you become a resident of the United States you are taxed similar to all US residents, citizens or not. I assume you plan to become a resident as soon as possible.

Then, you should consult Publication 901, US Tax Treaties which you can download from www.IRS.gov. There is a tax treaty and it states in part, on page 32: Income, other than a pension, paid by Switzerland or its political subdivisions or local authorities to an individual for services performed for the paying governmental body is exempt from U.S. income tax.
However, the exemption does not apply to payments for services performed in the United States by a resident of the United States who either:
-----Is a U.S. citizen, or
-----Did not become a U.S. resident only to perform the services.
Pensions paid by Switzerland for services performed for Switzerland are exempt from U.S. income tax unless the recipient is both a resident and citizen of the United States.
These exemptions do not apply to income or pensions for services performed in connection with a business carried on by Switzerland or its subdivisions or local authorities.

Tax Tables…other types of income subject to the treaty are at: www.irs.gov/individuals/international-taxpayers/tax-treaty-tables.