It is mustahabb to use the siwaak at all times, when fasting and when not fasting, at the beginning of the day and at the end. The evidence for that is as follows:
1 – al-Bukhaari (887) narrated from Abu Hurayrah (may Allaah be pleased with him) that the Messenger of Allaah (peace and blessings of Allaah be upon him) said: “Were it not that it would cause hardship to my ummah, I would have commanded them to use the siwaak for every prayer.”
2 – al-Nasaa’i narrated from ‘Aa’ishah (may Allaah be pleased with her) that the Prophet (peace and blessings of Allaah be upon him) said: “The siwaak purifies the mouth and is pleasing to the Lord.” Narrated by al-Nasaa’i, 5; classed as saheeh by al-Albaani in Saheeh al-Nasaa’i, 5.
These ahaadeeth indicate that it is mustahabb to use the siwaak at all times, and the Prophet (peace and blessings of Allaah be upon him) did not make an exception in the case of one who is fasting, rather the general meaning of the hadeeth includes both those who are fasting and those who are not fasting.
It is permissible to swallow the saliva after using the siwaak, but if anything comes out of the siwaak in the mouth, you should spit it out and then swallow the saliva, just as the fasting person is allowed to do wudoo’, then he should spit out the water from his mouth and then swallow his saliva. He does not have to dry his mouth completely from the water used for rinsing.
Al-Nawawi said in al-Majmoo’ (6/327):
Al-Mutawalli and others said: When the fasting person rinses his mouth, he has to spit out the water; he does not have to dry out his mouth using a cloth or the like. There is no difference of scholarly opinion on this point.
Al-Bukhaari (may Allaah have mercy on him) said:
Chapter: Using fresh or dry siwaak for one who is fasting … Abu Hurayrah said, narrating from the Prophet (peace and blessings of Allaah be upon him): “Were it not that it would cause hardship for my ummah, I would have commanded them to use the siwaak for every wudoo’.” Al-Bukhaari said: There is no difference between one who is fasting and one who is not. ‘Aa’ishah said, narrating from the Prophet (peace and blessings of Allaah be upon him): “The siwaak purifies the mouth and is pleasing to the Lord.” ‘Ata’ and Qutaadah said: he may swallow his saliva.
Al-Haafiz said in al-Fath:
By using this title, he refuted those who say that it is makrooh for a fasting person to use a fresh siwaak. This was preceded by Ibn Sireen’s likening the fresh siwaak to the water used for rinsing the mouth (in wudoo’).
“There is no difference between one who is fasting and one who is not” means also that there is no difference between fresh and dry. By stating this it becomes clear that everything narrated in this chapter fits the title. This is all summed up in the hadeeth of Abu Hurayrah, “Were it not that it would cause hardship for my ummah, I would have commanded them to use the siwaak for every wudoo’.” This implies that it is permissible at all times and in all situations.
“‘Ata’ and Qutaadah said: he may swallow his saliva.” This comment suits the title in the sense that the worst thing that may be feared from using a wet siwaak is that something may come out of it in the mouth. This is like the water used for rinsing the mouth; if the person spits it out from his mouth, it does not matter after that if he swallows his saliva.
Shaykh Ibn ‘Uthaymeen said:
The correct view is that use of the siwaak by one who is fasting is Sunnah at the beginning and at the end of the day. Fataawa Arkaan al-Islam, p. 468
The siwaak is Sunnah for one who is fasting throughout the day, even if it is fresh. If a person uses the siwaak whilst fasting and finds that he can taste it, and he swallows it or spits it out from his mouth and there is saliva on it, then he swallows it, that does not affect him. Al-Fataawa al-Sa’diyyah, 245.
He should avoid that which contains something that could come out of it, such as the fresh siwaak and those which have added flavours that come out, such as lemon and mint. He should spit out anything that breaks off in the mouth, and it is not permissible to swallow it deliberately, but if he swallows it accidentally it does not matter.
From Sab’oona Mas’alah fi’l-Siyaam (Seventy Issues Related to Fasting).
And Allaah knows best.