I used a Dremel with a cutting wheel. You'll go through a few discs. A good idea is to lay tape over the chrome and then mark your line on that so you reduce the chance of any slips marking the chrome. As much as possible cut from the inside, although the curve of the claw makes that difficult (it's also hard to mark it right). I cut off less than I needed to and then cut more; finished up with a couple of ribbons of off-cut. I wouldn't recommend that - took me 3 times as long - but certainly allow a little for a final trim and neaten. Be bold. The worst that can happen is you cut away a little more than you intended and no one but you will notice that.
The cut edge could rust a little, depending on where you are. I slid a candle across the edge of mine and it really didn't rust at all, but I'm inland and it is pretty dry here. I did slit a length of thin (2-3 mm) clear, tubing and put it over the edge. Looked like chrome. You can buy edging.