Is it possible to run an HDMI cable and attach the connector after the wire is run ike you would do with coaxial able or even speaker wires?
Anything is possible. However, it is not even remotely reasonable to be done in home. But, if the run isn't too long you could use a junction plate. The insertion loss and impedance mismatch for that short of distance shouldn't affect the waveform too much. Is your issue conduit related? If so, an HDMI over Ethernet might work out. Links below are examples. Choose what works best for you.