
I just bought a Draper Multi Tool 140W 230V (with the usual million and five tools and a flexible chuck. I believe they can be as cheap as £30 but more likely to be around £38. It's excellent, not noisy and if you keep it on speed 1 or 2 it will do the job very well. It's not cordless, but you can buy a much cheaper cordless version,
For whatever reason my youngest dog is very nervous of having his nails done, but he has been so good with this right from the beginning--I've just touched it to his nails so as not to alarm him, but he has been wagging his tail, bless him, he knows I'm doing my best for him :-)
I have a great "how to" guide that I picked up online (and now can't find the website) can email it to you if you pm me.