under powering a device

Do you have a real rms-capable meter? The unit might be pulling current in pulses. The higher current at lower voltage indicates another regulation inside in which case the power consumption will be identical, but just your measurement will be more off. You might also encounter less reliability with less voltage margin. To me it seems you should look at your measurement skills and also measure the really applied voltage at the gadget with a second meter after the amp-meter, because there will be some drop across it.

Hi, Bryan. Ban's right -- your measurements may be off.

I wouldn't do it. There are a lot of technical questions to consider. If the wireless unit (wireless what?) has an internal switching voltage regulator to supply a steady voltage to the circuit, a low input voltage could damage the switcher. Also, the regulator may not work properly at the lower input voltage, and the rregulator output power going to your wireless unit might not be properly regulated. That may mean that even if the power supply doesn't damage itself, the wireless unit might not work well.

When you're replacing wall warts with batteries or other power supplies, it's best as a rule of thumb to replace them with something as close to the original wall wart as possible. Solar arrays that put out 12VDC aren't uncommon. I'd go with one of those.

Good luck Chris