I subscribe to Rega, which is a Swiss not-for-profit air rescue organisation. You can become a “patron” for CHF 30.- per year via their website before you arrive. If a patron needs to be rescued by helicopter, anywhere in Switzerland, Rega waives the cost if this is not covered by an insurance policy.
In case of accident, Rega can be contacted by mobile phone via the European-wide emergency number 112, the Swiss ambulance service number 144, or directly on 1414. There is a free smartphone app. Also, their website states that their emergency radio channel (161.300 MHz) can be used by anyone throughout Switzerland to alert them to an emergency if this is not possible by telephone.
In the Wallis (the canton where Fiesch is located), rescues are not carried out by Rega themselves, but by Air Glaciers and Air Zermatt. However, it does not matter which company operates the helicopter; these remain free of charge for Rega patrons.