Well you have two very important numbers you need to match up when matching a diode to a driver (and picking the right ones of each).
1) Vf - "forward voltage" - this is the minimum voltage the diode needs to operate. Exceeding it by about 1v is generally not harmful and sometimes beneficial as long as you have adequate heat sinking. There are also two very important attributes you need to keep in mind.
2) Current - diodes put out more light the more current you supply them, but they have a minimum current and an absolute maximum current. Below the minimum current, called the Ith (Big I, little th) or Threshold Current, no lasing occurs. If you exceed the maximum current, the diode will be fried.
A) Diodes require a CONSTANT CURRENT driver. This means that the driver supplies the current it is set to, and lets the voltage sort it self out.
B) Drivers have what is called a "drop out" voltage. This is the difference in voltage between what you put in to it and what you get out of it. For example, a "DDL" LM317 driver has a drop out of 3V, so what voltage comes out of it is 3V lower than what you put in to it. For example if you wanted to use it to power a diode which has a Vf of 3V (like a typical red diode) you would need to input 6V to the driver to get 3V out. Low drop out drivers are called "LDO" drivers, and the actual drop out voltage varies from type to type as well as dependant on how much current they are set to.
*Buck/Boost drivers take a low voltage but high current input and put out a high(er) voltage and constant current output. A buck/boost driver like the Flexdrive could take in 3.7-4.2V from your Li-Ion battery and turn it in to the 4-6.5V that a 405nm diode would need. These drivers don't effectively have a voltage drop out, but they do require a very strong current source (battery).
As far as will that 100mW 405nm diode work with that "1W 445nm" driver... it depends on how low you can set the driver's output current. The voltage output from the driver should work fine, so it is all dependant on the lowest current the driver is capable of being set to, and if that current is within the range the diode accepts.