That is not a driver, it is just a round PCB. The LEDs are connected in a series/parallel configuration on the PCB so they can be driven by the 3 AAA batteries (in series at 4.5V).
Scratch the inside of the tube (where you removed the LEDs and the clear plastic lense) to the bare metal (you have to scratch through the anodization, until you see silver). One probe to the scratched place, the other to the battery pack connection. If you don't get a reading, punch the clickey switch on the bottom of the tube and try again.
To use this as a host, you need to build an insulated pill to connect to the battery connector (and a heatsink that will snug fit into the tube). Wire the pill connection to the driver B+ input (you need a driver with a common ground, Driver B- common to driver LD-). Sand away the annodization from the inside top of the tube, so that your heatsink will make electrical connection to the tube. connect the driver LD+ to the plus pin of the Laser diode, and the driver LD- to the Laser Diode negative pin (AND the case pin, if you are using a blue Laser diode). This will not work for IR diodes, as they are case positive, but, if you are foolish enough to want to use an IR diode, you should be able to figure out what changes would need to be made (it ain't very complicated...)