It may seem a non sequitur that having your head chopped off is grounds for being called upon for disorders of the throat, but then again maybe not. Of course it can also be attributed to the story that while in prison he performed a wondrous cure of a boy who had a fish bone lodged in his throat and was choking to death.
Whether he was a doctor of miraculous cures or not, we can depend upon his intercession to aid us in our need. We can call on many saints to plead for us in specific matters, but I do not believe that any of them would fail to hear and help us when we ask in Faith for anything - even if we wrongly associate patronage to them.
Hear, O Lord, the supplications your people make
under the patronage of the Martyr Saint Blaise,
and grant that they may rejoice in peace in this present life,
and find help for life eternal.
Through our Lord Jesus Christ, your Son,
who lives and reigns with you in the unity of the Holy Spirit,
one God, for ever and ever.
-- Collect, for the Memorial of St. Blaise