That is definitely possible. I think it makes use of only the 2.0 High-Speed data pair so you won't even need a flip-mux. That also means you will not need a PD controller unless you plan to operate at voltages > 5 volts.
Please have a look at this KBA on replacing existing Type-B connector with Type-C 'without PD'. The flip mux will not be needed.
Thanks this is useful