I just think, McCoy never had a medical tricorder. It looks much more like the old hypospray he used.
Did he even use a regular one? I'm not so sure. I just find it odd to have a prop that looks nothing like we've had before when the other two are fairly similar.
I just have a hunch this will turn out to be a hypospray or some sort of scanner.
Well, I have a hard time imagining an injector having internal wiring and so forth (though I also have a hard time imagining the need for commerical bar-code scanners all over the bridge, or lamps shining in peoples' faces, or round corridors inside a ship, or... etc, etc, etc...
I also doubt, very much, that this is the "tricorder." Again, hard to be CERTAIN, but since I'm not seeing any input controls or outputs (display, etc) it seems unlikely. More likely, this is the remote scanner "wand" which is PART of the medical tricorder (and yes, McCoy carried a medical tricorder... a different prop than Spock's "science tricorder" though largely similar... throughout TOS).
FYI, my view on tricorders has always been that they're modular... different plug-in components inside of a basic frame with a computer/control "head." Some of the modules include various high-power scanners (with a round "scanner unprocessed data display" on top... the round moire-pattern bit which is present on both the tricorder and communicator), a "data library" set (used on Spock's, but not on every version, in his case using round holographic-storage disks). The lower compartment contains various add-in cards, or additional sensors, and can also hold a removable scanner (of several possible types, most likely) with a charging/docking "socket" (as McCoy's did). Oh, and it would be possible to have a "communicator/log" card slotted in as well (for yeomen, for instance).
Think of the tricorder frame as a "motherboard and CPU" and the rest of it is the various other components of your PC.