The 4-pin circular (Foster) connector for microphones is very common.
Your local Radio Sheck likely has that 4-pin microphone connector in their parts bins.
FOX-TANGO : FT-series microphones, including your YD-844A with wiring diagram
http://foxtango.org/ft101/foxtangoft101acc.htmThe YD-844 desk top microphone and the mobile microphone was available from Yaesu in high and low impedances, using a shielded microphone cable terminating into a 4 pin microphone connector for use with the FT-101 or a 3 prong 1/4 inch stereo type jack for use with the FL-101 transmitter .