Pretty well any of the David Tait style parallel port programmers work perfectly from two 9V batteries - I've run various ones for years from two Duracell MN1604's. The P16PRO40 works fine like that.
There are no problems whatsoever, it's a far cleaner supply than a wallwart - one of my most common answers to support queries is to try two 9V batteries and see if it works then!.
The batteries last for ages - PROVIDING YOU ONLY CONNECT THEM WHEN USING THEM - if you leave them connected permanently they go flat in a few days.
I think the LED's in the programmer need more current then the programming itself, include an option to disable the leds and you'll do months with one set of batteries...