It honestly sounds like more of an anxiety issue than an actual neurological stutter. The way you’re describing it sounds like the idea of picking up the phone stresses you out which hence gives you anxiety while talking on the phone. The best advice I could give you, is just try to relax get some confidence. The person on the other side of the phone has no clue who you are you could stutter all you want & it’s not gonna matter. Ik confidence is easier said then done. But I believe you could gather it up.