An update to this issue. I tried it with a 6.35mm mono tele plug and it almost worked. I get some signal, but very, very low. I believe this is because the UR22 treats any 6.35mm plug as a line-in signal.
It looks like the only way for a UR22 to accept a microphone signal is through the XLR connector. I’m currently thinking I need to solder my own Stereo3.5mm-UnbalancedMonoXLR FemaleToMale connector for this.