Praise be to Allah.
The one who is fasting should guard his hearing and sight from that which is haraam, because of the report narrated by al-Bukhaari (6057) from Abu Hurayrah (may Allah be pleased with him), who said: The Messenger of Allah (blessings and peace of Allah be upon him) said: “Whoever does not give up false speech, acting in accordance with it, and ignorance, Allah has no need of his giving up his food and drink.”
Ahmad (8856) narrated that Abu Hurayrah said: The Messenger of Allah (blessings and peace of Allah be upon him) said: “There may be a fasting person whose share of his fast will be hunger and thirst, and there may be a person who offers voluntary prayers at night (qiyaam) whose share of his qiyaam is a sleepless night.” Shu‘ayb al-Arna’oot said in Tahqeeq al-Musnad: Its isnaad is jayyid.
Ibn Abi Shaybah narrated in his Musnad (8882) that ‘Umar (may Allah be pleased with him) said: Fasting does not mean refraining from food and drink only; rather it also means refraining from lying, falsehood, idle speech and swearing (false) oaths.
He narrated a similar report (8884) from ‘Ali (may Allah be pleased with him).
And he narrated (8883) that Maymoon ibn Mahraan said: The easiest part of fasting is refraining from food and drink.
And he narrated (8888) that Ibraaheem an-Nakha‘i said: They used to say: Lying breaks the fast.
Ibn Hazm (may Allah be pleased with him) held a similar view, and said that deliberately committing sin breaks the fast. See: al-Muhalla (4/304).
So a fast in which the fasting person does not guard against haraam things is an imperfect fast.
Ibn Rajab (may Allah have mercy on him) said: One of the early generations said: The easiest part of fasting is refraining from food and drink.
Jaabir said: If you fast, then let your hearing, your sight and your tongue also fast (refrain) from lies and haraam things, and stop annoying your neighbours, and be dignified and calm on the day of your fast; do not make the day you fast and the day you do not fast be the same.
In Musnad al-Imam Ahmad it is narrated that two women fasted at the time of the Prophet (blessings and peace of Allah be upon him), and they almost died of thirst. That was mentioned to the Prophet (blessings and peace of Allah be upon him) and he turned away, then those two women were mentioned to him again. So he summoned them and commanded them to vomit, and they vomited a vessel’s worth of pus and blood, and pieces of fresh meat.
The Prophet (blessings and peace of Allah be upon him) said: These two women fasted and refrained from what Allah had permitted to them, but they broke their fast on that which Allah has forbidden to them; one of them sat with the other and they began to eat the flesh of the people [i.e., backbiting].”
End quote from Lataa’if al-Ma‘aarif, p. 155.
The hadith quoted has a da‘eef (weak) isnaad.
Whatever the case, if you want to fast properly, then you must give up this work during Ramadan, so that your heart, sight and hearing may be safe from falling into that which is haraam.
If watching these videos results in provocation of desire and emission of maniy (semen) as a result of repeated watching, then there are two scholarly views as to whether the fast is rendered invalid.
In al-Mawsoo‘ah al-Fiqhiyyah (26/267) it says: The Hanafis and Shaafa‘is are of the view that emission of maniy or madhiy (prostatic fluid) as a result of looking at or thinking of [that which provokes desire] does not invalidate the fast. On the other hand, the more correct view according to the Shaafa‘is is that if a person usually ejaculates as a result of looking, or looking repeatedly, then if he ejaculates whilst fasting, then this does invalidate the fast.
The Maalikis and Hanbalis are of the view that emission of maniy as a result of persistent looking invalidates the fast, because it happens as a result of an action that is pleasurable, and that it is possible to avoid.
With regard to emission of maniy as a result of thinking, it invalidates the fast according to the Maalikis, but according to the Hanbalis it does not invalidate the fast, because it is not possible to avoid it. End quote.
With regard to the emission of madhiy as a result of repeated looking, it does not invalidate the fast.
Al-Mirdaawi said in al-Insaaf (3/302): What may be understood from the phrase “or he looks repeatedly and emits” is that if he looks repeatedly and emits madhiy, that does not break the fast. This is the correct view, and it is the view of our madhhab and of most of our companions. Az-Zarkashi said: It is the correct view. It says in al-Furoo‘: The view that it breaks the fast is more in harmony with our madhhab, like the view on touching. End quote.
Our advice to you is to leave this job, because even if it results in reducing evil for minors as you said, its impact and negative effects on your heart and soul cannot be denied, and nowadays minors can easily access material that is worse than what is being kept away from them, so the hoped-for benefit of this work is not great, and warding off evil from yourself takes precedence over benefitting someone else.
And Allah knows best.