The difference between the UNO and Pro Micro is that the serial pins are reversed. On UNO it's 0 for RX and 1 for TX, on Pro Micro pin 0 is TX and 1 is RX. If you swap the HM-10 wires it should work.
The difference between the UNO and Pro Micro is that the serial pins are reversed. On UNO it's 0 for RX and 1 for TX, on Pro Micro pin 0 is TX and 1 is RX. If you swap the HM-10 wires it should work.