To connect the AT3031 to a wireless transmitter, I am looking for a battery-powered phantom power supply. The transmitter is an AT U100.
The application is a shoot where there is no house sound system that could power the mic, and it is not practical to run an XLR cable from the mic to my cam.
B&H has battery-powered phantom power supplies by ART and Rolls. Is either a good choice? Is there a better solution for my application?

That should work, although with any wireless application you should test it ahead of time. There are always potential problems with RF from the transmitter interfering with the phantom supply or the mic.
Sometimes the phantom supply can also reduce the amount of RF the transmitter is successfully sending out.
Then there are the normal things that can cause problems with wireless, such as multipath, interfering frequencies, etc.
Even if everything works perfectly, sending the AT3031 through the wireless will reduce its frequency response and dynamic range. For voice this should be ok, but for music would be noticeably inferior.
I know you said the house doesn't have a sound system, but does it have balanced house wiring? Many times that can be used to greatly reduce the amount of cable you have to run.