I'd be very wary of using AC adaptors (wall-warts?) for two major reasons.
1. A 9volt adaptor will be supplying 9volts at its rated output - in your case 800mA. The regulation of the tiny transformer is pretty poor, so by only drawing 300mA the output voltage could be waaay high - maybe damaging your radio by either over-stressing voltage sensitive parts, changing the operating parameters of amplifiers etc or getting the thing overheated in the voltage regulator stages.
2. A lot of power supplies are switch-mode types, which radiate high frequency noise over a wide range of frequencies. This may be overriding your incoming signal. Do you have to adjust the squelch when using the AC power supply? That's usually a clue.
What majoco said is very true.
The exception here is only if the wall wart is a truly regulated type that puts out a regulated voltage independant of the load placed upon it.
It the wall wart is truly a regulated type, then it is ok to use one with a higher current rating as the output voltage will always be the same. Doing this can also cure some of the noisy switching types if the orignal design was barely above the devices current requirements. A higher current regulated model will not need to work as hard.
As majoco stated, a standard unregulated wall wart depends upon a certain amount of current be drawn from them in order to bring the voltage down to an acceptable level. This is how they work by design.
I've seen many so called 12 volt wall warts that put out well over 25 volts when measured with no load. If you do not put enough load on the output, the voltage may only drop to say 18 volts which can kill things that are before any internal regulators like back lights and other components that may not be regulated internally at all.
And also as majoco said, switching type wall warts (very common these days) are notorious for emmiting RF noise. Some will completely wipe out a DSL internet signal for example. They usually do not cause many problems for a typical scanner type radio but they are well known to be bad for those into HF monitoring. Some are designed better than others also but there is no known database of ones to avoid.
I myself get rid of them and run everything I can from a bank of batteries that are constant charged from a large linear type supply. This gives me no noise from the switching type supplies plus it keeps me running when the power fails which is often here in the winter months.
I regulate my main 12 volt bank down to 9 and 5 for the devices that need those lower voltages.
For the switchers that I must keep running, I run them through an analyzer and make notes of any unwanted emmisions so I can kill them when I'm going to do any monitoring of the ranges they spew their crud within. Most all of the modern day scanners do come with switching type supplies and amazingly, the Icom R75 receiver I purchased some time back also came with a switcher supply. If I'm not mistaken, the paperwork that came with the R75 mentioned the fact that the switcher supply may interfere with certain frequencies so that was nice of Icom too mention that fact.