Many golf courses use Bent Grass for their putting greens. It can be maintained as short as 1/2" inch high, but you'll have to cut it every 3-4 days. It can be mowed to a very short length without damage.
As far as cutting tools go, you could try something like the Skil Isio Shrub and Grass Shear. I've got one and it works great for maintaining small shrubs. It even works on my holly bushes as long as I trim them regularly.
I've never used the grass shear attachment since I've got a 1/2 acre lawn, but if it works as well as the shrub attachment, I'd give it a try. (Note: I picked this up on sale for $30. Not sure if I'd pay the $70-100 it's going for online.)
If you don't want to spend the money for a power tool, there's always manual grass shears for around $15, but I don't know how much faster they'd be than regular scissors.