Usually the rental car company pays the fine and charges your credit card automatically.
For that 'low' SFr 60 fine you are not obliged to give the police the name auf the driver, only the name of the bank account holder that the money comes from is asked for.
Usually the swiss police gives you 30 days payment grace period - after that the 'case' is forwarded to court and the fees and charges increase 'dramatically'.
If you want me to pay that SFr 60 amount for you in Switzerland, contact me by FlyerTalk email (and then send me the papers by air mail) - and in return I will give you my HSBC USA account number to pay me the equivalent US$ amount in your country.