If you want to run the Arduino off the 19V supply, you can use a voltage regulator like an LM7809 or LM7808 to step the voltage down and dissipate most of the waste heat. Depending on what's connected to the Arduino, you might or might not need to put a heat sink on the regulator (I'd probably do it, since it only costs a quarter or so, but I tend to be overly-conservative about such things). The 19V supply should be clean enough that you won't need to do all the noise- and spike-protection steps I mentioned earlier, though.
Ran