Praise be to Allah.
There is nothing wrong with wearing a watch on either the right or left hand . A man can choose whichever is easier for him, and neither can be regarded as being contrary to the Sunnah.
Shaykh ‘Abd al-‘Aziz ibn Baz (may Allah have mercy on him) said:
“There is nothing wrong with wearing a watch on either the right or left hand, like a ring, because it is proven that the Prophet (peace and blessings of Allah be upon him) wore a ring on his right hand and left hand.” (Fatawa Islamiyyah, 4/255)
Shaykh Muhammad ibn Salih al-‘Uthaymin (may Allah have mercy on him) said:
“Putting a watch on the right hand is not better than putting it on the left hand, because a watch is like a ring, and there is no difference between putting a watch on the right hand or left hand. But undoubtedly putting it on the left hand is easier with regard to correcting it and looking at it, and it is safer in most cases, because the right hand moves more so it is more likely to cause damage to it.
The matter is broad in scope, so we should not say that the Sunnah is to wear it on the right hand, because it is narrated in the Sunnah that it is permissible to wear a ring on both the right and the left hand, and a watch is like a ring.” (Al-Sharh al-Mumti’, 6/110)
And Allah knows best.