Should one marry during umrah in order to have a mahram?

It is not needed. The Saudi Minister of Hajj and Umrah announced in October 2022 that women may perform Hajj and umrah without a mahram if accompanied by trustworthy women or a safe group (Arab News, citing SPA). Package conditions and Tabung Haji policy for Malaysian pilgrims (check with the authorities of the country concerned). Moreover, according to the majority of scholars including the Shafi'i and Hanbali schools, a marriage contract is invalid while in ihram (Sahih Muslim, Kitab an-Nikah). An umrah or tourist visa is also not a route to residence; a marriage without approval gives no residence permit, and such marriages often cannot be registered. An undocumented "under the table" marriage leaves the wife and children unprotected. See Saudi Arabia.