If the Muslim is not able to visit the graves except on Fridays because he is working on all other days of the week apart from Friday, then it seems that there is nothing wrong with that because by doing that he is not singling out Friday as having an advantage over other days. He is not doing that because he singling out Friday for that purpose; rather it is because it is his day off.
Shaykh Ibn Jibreen (may Allah have mercy on him) was asked: Friday is a day off for us; if we single out this day or a few hours of it for visiting graveyards, does this come under the heading of bid‘ah (innovation)?
He replied: It does not come under that heading, because there were some reports which speak of visiting graveyards on Friday. … So long as you did not deliberately single out this day and this is when you have free time, then there is no sin on you in sha Allah. There are some reports that speak of singling out this day and of its virtue, but they are not proven. End quote from Fataawa Ibn Jibreen.
Shaykh Ibn ‘Uthaymeen (may Allah have mercy on him) said: The apparent meaning of the evidence indicates that it is general in application and that it is makrooh to single it [i.e. Friday] out for fasting, whether it is an obligatory fast or a naafil one. But if a person has work and is not free and he cannot make up his fasts except on Fridays, then in that case it is not makrooh for him to single out this day for fasting, because he needs to do that. End quote from Majmoo‘ al-Fataawa, 20/55
Singling out a day for observing a nafl fast is permissible, unless it is a Friday or Saturday , or it is the day of ‘Ashura which is the tenth day of al-Muharram, in which case it is mustahabb to fast the day before or the day after as well.
As for Sunday, Monday, Tuesday, Wednesday or Thursday, there is nothing wrong with fasting them on their own, rather it is Sunnah to fast on Mondays and Thursdays .
Al-Bukhari (1985) and Muslim (1144) narrated that Abu Hurayrah (may Allah be pleased with him) said: I heard the Prophet (peace and blessings of Allah be upon him) say: “No one of you should fast on Friday, unless he fasts (a day) before it or after it.”
According to a report narrated by Muslim: “do not single out the day of Friday for fasting, unless that coincides with a fast that one habitually observes.”
Al-Nawawi (may Allah have mercy on him) said: “These ahadith appear to support the view of the majority of the companions of al-Shafi’i, which is that it is makruh to single out Friday for fasting unless that happens to coincide with a fast that one habitually observes. If he joins it to a fast on the day before or the day after, or it coincides with a day that he habitually fasts, such as if he vowed to fast on the day that a loved one was healed for the rest of his life, and that happens to be a Friday, then it is not makruh, because of these ahadith.”