Sayyidah Aishah (may Allah be pleased with her) narrates that the Prophet (peace and blessings be upon him) would sometimes apply kohl while he (peace and blessings be upon him) was fasting.
Sa'id al-Zubaydi is one of the unknown (majhul) teachers of Baqiyyah, who narrates alone what is not corroborated. It has also been narrated marfu' from Anas bin Malik, with a very weak chain, that he saw no harm in it.
Hadith Referenceالسنن الكبرى للبيهقي / كتاب الصيام / 8259