Single cable for dual Ethernet plus power (PoE)
Firstly you will need to check your end devices are 802.3af mode b compliant, otherwise you can't inject the power onto a discrete pair, but instead if they are mode a, you need to put the power onto the data pair which is usually a function of the switch.
With regards to UTP. It is possible you might be able to use non twisted cables if the distance is short, your devices will put up with a lot of dropped packets, sub 10Mbit speeds are ok and you don't have too much issue with external EMF sources.
But I would be much more inclined to simply run two shielded UTP cables.