During the 1346 Battle of Crecy, the blind King John of Bohemia is recorded by chronicler Jean Froissart as having gone into battle and entered the thick of the fighting. Along with his attendants, tied by their bridles together, the King entered battle against the English and was killed.
Was he successful? No. But he was prominent. Froissart dedicates a significant amount of space in his account of the Battle of Crecy to remembering this man's action. It is implied to be a highly chivalrous and noble event, despite its apparent stupidity. As much as he isn't a capable fighter without sight, John of Bohemia fits the definition of a 'blind swordsman'.
The valiant and noble king of Bohemia, known as my lord John of Luxembourg, for he was the son of the emperor Henry of Luxembourg, heard that the battle was begun; for although he was there fully armed and equipped, he could not see a thing. So he asked the men at his side about the dispositions of their men. They told him, "My lord, this is how things stand. All of the Genoese are defeated and the king has ordered them to be killed. Notwithstanding that, between our people and theirs there is such a riotous melee, for they are falling over each other and really getting in our way." "Ha," responded the king, "this is a little sign for us." After that he asked for the king of Germany his son, "Where is lord Charles, my son?" They replied, "We do not know my lord. Though we believe that he is elsewhere on the field and engaged in combat." Then said the king most courageously to his men, "Lords, you are my friends and my companions. Today I beg and request of you specially to lead me forward so that I may strike a blow with my sword." Those who were at his side agreed.
...he advanced so close to his enemies that he landed a blow with his sword, indeed three of four; he fought very courageously as did all those who were with him. They advanced so far into the English ranks that all remained there, and the next day were found surrounding their lord, their horses all still fastened together.