Is it permissible to wear a watch that contains a small amount of white gold?

Firstly: 

White gold is the same as the well known yellow gold, but some other metals such as palladium have been added to it to change the colour to white. This is what the experts say, and that has been discussed in the answer to question no 68039 

As this is the case, it is haraam for men to wear it even if it is a small amount, because of the hadeeth narrated by Muslim (2090) from Ibn ‘Abbaas (may Allaah be pleased with him) which says that the Messenger of Allaah (peace and blessings of Allaah be upon him) saw a gold ring on a man’s hand. He took it off and threw it aside, and said: “Would one of you go and pick up a live ember of fire and hold it in his hand?” After the Messenger of Allaah (peace and blessings of Allaah be upon him) had left, it was said to the man: Take your ring and benefit from it (by selling it). He said: No, by Allaah, I will never pick it up when the Messenger of Allaah (peace and blessings of Allaah be upon him) has thrown it aside. 

Abu Dawood (4075), al-Nasaa’i (5144) and Ibn Maajah (3595) narrated from ‘Ali ibn Abi Taalib (may Allaah be pleased with him) that the Prophet (peace and blessings of Allaah be upon him) took a piece of silk in his right hand and a piece of gold in his left and said: “These two are haraam for the males of my ummah.” Classed as saheeh by al-Albaani in Saheeh Abi Dawood. 

Al-Nawawi (may Allaah have mercy on him) said in Sharh Muslim: As for gold rings, they are haraam for men according to scholarly consensus. The same applies if they are partially gold and partially silver. End quote. 

The Standing Committee for Issuing Fatwas was asked: It has become common among some people, especially men, to use that which is called white gold, which is used to make watches, rings, pens and so on. After asking the jewellers and goldsmiths, we found out that white gold is actually the well-known yellow gold, to which a certain metal has been added, 5-10%, to change its colour from yellow to white, or some other colour, which makes it look like another kind of metal. Use of this has become very widespread in  recent times, and many people are confused about using it.

They replied: 

If the situation is as described, the gold which is mixed with other metals still comes under the ruling that it is haraam to differentiate in weight or measure when selling it for gold of the same type, and the exchange must be completed in one sitting, whether it is sold for gold of the same type or for silver or cash. It is haraam for men to wear it, and it is haraam to make vessels out of it. Calling it white gold does not change these rulings. End quote. 

Fataawa al-Lajnah al-Daa’imah (24/60) 

Secondly: 

There is nothing wrong with wearing a watch which contains diamonds, because the basic principle is that they are permitted, and there is no evidence to suggest that they are not allowed. 

The Standing Committee for Issuing Fatwas was asked about wearing valuable watches which contain diamonds or gold. 

They replied: Wearing diamonds is permissible for men, and we do not know of anything wrong with that if they are pure and there is no gold or silver with them. End quote. 

To conclude: if the watch is free of gold then it is permissible to wear it, otherwise it is not permissible. 

And Allaah knows best.