Should I worry, or will it be fine

it depends on what the device is and how it was designed.

it's also important to know what the amp requirements of the device are and how many amps the power supply can provide.

personally I would not mis-match power supplies with devices.  a lot of times it won't cause problems, but on the occassion it does - why risk it?

I agree with Beagle. I would not mis-match power supplies. A 9 volt supply is rather common - so I would get one to be safe.

Both PSU and Trigger finger are 500mA

Just trying to get rid of the sea of cables. I tend to have my midi cable and psu cable for my wind synth cable tied togther, to stop them tangling. As I never play the Trigger finger and wind controler together, at the moment, presents and easy solution in unplugging one and attaching the other 

What often happens is that your external power supply will feed into some sort of voltage regulator inside the unit you are powering up. The voltage the comes out of the regulator (and feeds the internal circuitry) will often be little lower than the voltage going in. The difference in voltage going into the internal regulator and coming out of the internal regulator will be smallish and is turned into heat but the regulator is usually designed to cope with that.

But when the voltage going into the regulator is a lot higher than 9 volts what happens is that the internal regulator will still output the same voltage as it did before (into the circuitry) except now there is a much larger voltage difference across the regulator and as result it will get hotter and could fail under the extra heat is has to dissipate. You are straining the internal regulator now.

So best to feed in the correct DC voltage that is being asked for. Many 9 volt power supplies actually put out a higher open circuit voltage than 9 volts so the internal regulators are often dealing with a slightly higher than normal input voltage anyway. Why make it worse with a higher voltage supply. eg a 12 V DC supply could be putting out 15 volts or more open circuit. 

With current ratings feeding a device that requires 500mA with a power supply that is only rated at 500mA also is not a great idea either. You will find the power supply might get a bit hot under these conditions. If I needed to supply 9 volts at 500 mA I would use a power supply rated at 9 volts but closer to 1A for extra current. Then it would only run luke warm which is a better option. A lot of the newer switchmode DC supplies these days are excellent and can supply very regulated voltages at quite high currents and run very cool at the same time.

Cool thanks for the explanation. I used to run a whole load of rackmount synths, so used to have a stake of these for different voltage, ampages and AC/DC outputs, and would put coloured stickers on them. Some weren't the originals, so was often a case of if this one works with that, then I went with it. I rarel had a falure and where I did it was the PSU, and never the device. But as this happened with the original manufacturer matched supply, I've not had any real indictation to get an idea.

The device is meant to able to run on USB, but there's a conflcict going on, I seem to get more issues trying to run it with the external soundcard, which obviosuly takes priority. Sometimes it's not being recognised as a device, but I have a keyboard that uses the same m-audio drivers and that works fine. When it is being recognised, it's not outputting midi, so the usb can suply the power, and I can connect the midi out to the soundcards midi in, and that works fine. I happen to be short on usb inputs, so decided on giving up on the useb and treating as a midi device using midi and and a PSU, that means the keyboartd can stay perminantly plugged in and all is sorted.

I did some reading on USB today.  USB is lower than 9v so clearly it's having to deal with 9v as more than enough as it is. I guess as you say, it's probably regulationg that down to the same as USB or thereabouts.

I'll get a PSU as advised. Thanks

Some devices seem to be protected and others are not. I fried a most excellent Korg Poly 800 ( worth $1,200 at the time) in 2 seconds flat when I used the wrong wall wart by mistake. I always figured they should make the ends so they will or won't fit and standardize them. I have always stayed with using a Boss Power supply for all my 9 volt pedals. Why take a chance.