Switch port maximum output power
Do you mind voiding your HP warranty by modifying internally or do you want to farm power from the signal or maybe add DC externally via an adapter.  Depending on your model you might be able to modify it easily to add POE to some ports. Generally it is 48V 10W min per port but in your case you don't need that so you either customize or pay for off the shelf $$.

I designed a 16 chan. POE rack for AVAYA (nee Lucent) over 10 yrs ago by 3rd party contract so I have some familiarity.

You only need a few diodes to insert and extract DC if you have centre tapped transformers already in the HP switch. It must be a floating DC power supply.

Here is a basic interface example showing extraction from both lines. You only need one bridge per port and possible only 1 diode if you already know the polarity and aren't using crossover cables.