Old woman traveling without a mahram for umrah

It is not permissible for a woman to travel the distance of 78 km or more without a mahram. Hence, if you do not have a mahram accompanying you during the safar, it will not be permissible for you to travel.

Severe warnings have been sounded in the Ahaadith for a woman travelling without a mahram.

Hazrat Abdullah bin Umar (radiyallahu anhuma) reports that Rasulullah (sallallahu alaihi wasallam) said: "It is impermissible for a woman to travel for the safr distance of three days unless she is accompanied by a mahram." (Bukhaari #1086)

Hazrat Abu Saeed (radiyallahu anhu) reports that Nabi (sallallahu alaihi wasallam) said, "It is not permissible for a woman who believes in Allah Ta’ala and the day of Qiyaamah to travel for the safr distance or more unless she is accompanied by her father, brother, husband, son or any other mahram." (Tirmizi #1169, Abu Dawood #1728)

Hazrat Abdullah bin Umar (radiyallahu anhuma) reports that Rasulullah (sallallahu alaihi wasallam) said: "A woman travelling with her slave (or any other non mahram) is bringing destruction to her Deen." (Majmuz Zawaaid #5302)

And Allah Ta'ala (الله تعالى) knows best.