Answered by: Maulana Muhammad Afzal Hussain
Can a woman perform Umrah without Abaya?
بِسْمِ اللهِ الرَّحْمنِ الرَّحِيْم
In the name of Allah, the Most Gracious, the Most Merciful
Although men have a prescribed dress code for Hajj that consists of two pieces of unstitched cloth, there are no similar specific garments for a woman.
Instead, it is advised that women follow the normal dress code of Islam and wear clothes that are loose-fitting, fulfill the requirements of Hijab, and do not call for attention. Any type of garment can be worn in Ihram by women, but the face has to be uncovered. 
Many women choose to wear abayas, but this is not obligatory. Therefore, a woman can perform Umrah without Abaya.
Only Allah knows best
Written by Maulana Muhammad Afzal Hussain
Checked and approved by Mufti Mohammed Tosir Miah
Darul Ifta Birmingham
 [See: Aap ke Masail Aur Un Ka Hal by Shaykh Yusuf Ludhyanvi, vol: 2, Page: 15, Publisher: Bangladesh Islamic Centre Dhaka]