Praise be to Allah, and may Allah’s peace and blessings be upon the Messenger of Allah, his family and his companions.

Wa alaikum assalam wa rahmatullahi wa barakatuh.

To proceed:

In response to your question, I say :

 
The time after Asr prayer is singled out because it is from the times that swearing becomes emphasized. The oath is emphasized for reasons which are to do with time, place or situation. The emphasis to do with time is after Asr prayer, thus the oath after Asr prayer is emphasized. To this end, the Messenger of Allah (peace be on him) mentioned it in the hadith. However this does not mean that the ruling is only specific to this time, meaning to say there is no problem in someone taking an oath after Dhuhr prayer, that is not correct. The time after Asr prayer was only mentioned because it is a time where the oath is emphasized, but this does not negate the ruling during other times.
Therefore the specification given to the time after Asr prayer is because it is a time where the oath is emphasized, and this is not a permission to give a false oath on commodities or anything during other times. This is according to the hadith: “Whoever takes an oath when asked to do so, in which he may deprive a Muslim of his property unlawfully, will meet Allah who will be angry with him (i.e on the day of judgement).”[1] The ruling in the hadith is not only restricted to the time after Asr prayer but rather it is restricted with the act itself.
Another hadith narrated by the Messenger of Allah (peace be on him) says: “If anyone seized - by his oath - what rightly belongs to a Muslim, Allah has made the Hell-fire compulsory for him and forbidden for him the Paradise." A man asked, "O Allah's Messenger (peace be on him), even if it were something insignificant?" He replied, "Even if it were a stick from an Arak tree.”[2] This hadith clarifies the great danger of seizing peoples’ wealth and that a person is aware of the gravity of a false oath to the extent that the people of Jahilliyah (ignorance) used to avoid taking false oaths due to fearing its consequences and that Allah would become  angry and hasten the punishment for those who took false oaths.