Is it impermissible for women to run/jog between safa and marwa (during hajj/umrah saee)?

According to the Islamqa women do not run between safa and marwa as it may lead to immodesty. > Women, however, do not run, because they are required to cover themselves and be modest, and running may expose their bodies and their charms Furthermore they say : > Ibn al-Mundhir said: The scholars are unanimously agreed that women do not have to trot around the Ka’bah or between al-Safa and al-Marwah From my understanding, Islamqa suggests its not obligatory for the women to run/jog. 1. Is it **impermissible** for her to run/jog out of remembrance for Hajar ? (provided she can manage to not uncover) 2. if yes, is it a sunnah(rewarding) if she runs/jogs? I haven't found a prohibition from Hadith hence my question since the very act men are mimicking was done by a woman (Hajar). (Looking for Sunni answers)