It should be clear that a person who is offering the pilgrimage cannot do the `Umrah on these days. However, a person who is not doing the pilgrimage may offer the `Umrah at any time, even on the day of `Arafat, or on the Day of Sacrifice.
Many pilgrims take the opportunity of being in Makkah in order to do `Umrah after the Hajj. This particularly applies to those who opt for the ifrad method of Hajj. These pilgrims should wait until the 14th of Dhul-Hijjah when they should go out to At-Tan`eem or any point at the boundaries of Al-Haram area where they should then enter into the state of ihram, making their intention to do the `Umrah, and return to Makkah to fulfill its duties.
However, a person who is not performing the Hajj may offer the `Umrah at any time, even on the day of `Arafat, or on the Day of Sacrifice. Take, for example, the case of a person traveling from Europe or Africa to Pakistan, India, or any Eastern destination. He can make a stopover at Jeddah for one day or a few hours, during which he wishes to do the `Umrah. There is nothing to prevent him from doing so, as long as he has the necessary permission (the appropriate visa). If such a person arrives in Jeddah on the day of `Arafat, he may go ahead and do the `Umrah. There is nothing to prevent him from doing so.
Allah Almighty knows best.