You can set up a new AG or GMBH through a fiduciary services.
They will appear in public registers as owners of the new company, and your name will never appear.
Then they will provide a nominee swiss national/resident as director of the company. Swiss laws request at least one resident director.
In the case of nominee director the fiduciary will check carefully the management of company activity, so they will have executive control of bank account (sending and receiving funds), and issuing of invoices, you as UBO will give them instructions what to do but they will be able to refuse some actions or asking more info.
The problem with anonymity is with opening the bank account, now all banks in Switzerland want to know who is the real UBO of the company, this information will be kept secret, but in case of tax or criminal investigation coming from abroad they will declare everything, swiss privacy is only a sweet memory.
Price for incorporation of a new company varies from 5.000 to 8.000 swiss francs, and then you have to pay for fiduciary services, nominee director, registered office, accounting, tax and vat filing, everything will cost at least 10.000 francs per year.