Probably.
The modules are not specifically for phone pairing at all. It is just that that is the most common approach, with the phone acting as master. All that means is that the phone app initiates the connection.
In your case Arduino is the master, i.e. IT initiates the connection, and HM-10 is up to that. Indeed this is surely a simple SPP datastream job, and the so-called "fake" CC2541 HM-10 should be fine. The UUID is essentially the same as an HC-05 MAC address, and does not bring its own problems.
I have little experience with BLE, and you will probably get more enlightenment on the Martyn Currey website.