FWIW.
The OP can not take the chance of changing the wall outlet to a GFCI duplex outlet. No way...
The OP could lose the power to the outlet just like the dead one that is now blanked off.
There is a very good chance the outlet is used as a feed through box. Circuit in, circuit out. Four old rubber cloth covered wires. Chances of moving the old conductors around, removing the old outlet, and wiring the new GFCI outlet without the old brittle insulation falling off at the steel cable support bracket or breaking falling off the wires at the BX steel armor are slim to none. Or the wires just breaking off at the support bracket from disturbing them.
Not only the outlet the electrician in trying to install the GFCI outlet in, how many other outlets could/will lose power in the process?
Not necessarily a problem, a box extension would need to be installed for the GFCI outlet because of the shallow depth of the switch box.
That’s why I suggested a plug-in type 15 amp GFCI.