Unfortunately you’re in a crisis counsellor job role, and people threatening suicide would come under a crisis. Calling these people/other centres etc is totally necessary as someone’s life is in danger. It might be worth you looking into other areas of employment where use of the phone isn’t as important as this job. Generally I would say that the more you practice/use the phone, the better your stutter will come as you’re essentially desensitising yourself to the situation that you fear.