Anthony Joshua has fast hands? You must be talking about another Joshua. The one who loves to fight old men has slow hand speed and now technique or skill. Bird would easily make Joshua look like a fool and win on points.
Joshua's already proved himself a level above the likes of Fres Oquendo, Jameel McCline and DaVarryl Williamson who Byrd struggled badly with, Byrd's become a tad overrated IMO, he also wasn't the defensive genius people believe he was either, he was quite hitable.
AJ wins. But the fights you brought were when Byrd lost some speed and reflexes. Watch his fights vs Tua and Vitali, guy had an excellent defensive skills.