The buzzers have arrived. I am not feeling like working with them, too much, but I was able to make theses quick observations...
CMI-1295-05TH
I think Josh noted that the canister might be a hair wide, on the dimension across the flats, to fit completely into the barrel of the probe socket. This is true. The canister is about 0.5mm too wide.
Josh also mentioned that the side of the canister might be sanded off, to make it fit. I have my doubts that this could be done, without breaching through, because the buzzer's walls are particularly thin.
However, I do believe that the this buzzer could easily be glued to the top of the flats. There does appear to be room between the top of the flats and the metal front case bracket. No guarantees = You will need to do your own measuring.
Additionally, the question about the ambient noise created by this type buzzer (magnetic) has not been sorted out.
PKLCS1212E2400-R1
This buzzer is a piezo type, so there is no compatibility issue. At 12x12x3mm, it fits nicely across the flat top of the probe socket hole.
However, there are a few points to consider in mounting it.
1) The sounding hole is on the same side as the pin pads (Blue arrows.)
2) The sounding hole is offset from the center to the edge (Red arrow.) The socket hole has room to align the sounding hole fully in the opening, but care will be needed in seating the case. Gluing it in would be simple enough.

The Original Buzzer
I sized it up, a bit more. I still believe that it will fit within the open space in the plastic face plate. But, you will need to confirm this for yourself.
Next Step
I am liking the PKLCS1212E2400-R1 best of all, as far as mounting a buzzer is concerned. I will do some sound level tests with it. If it is acceptable, I will likely give it a try.