When photographing artwork, sharpness over the entire focal plane is what's important. Some cameras are only sharp in the center, and that won't work for what you're doing. Your best results will probably come from a camera with a large aperture lens that you can stop down one or two stops. Point & Shoot cameras with large aperture lenses are not exactly your mainstream product, but there area some.
But you also should probably get something with a high resolution image sensor, which narrows down your selection even further.
There's the 24MP
Sony RX1 with the Carl Zeiss 35mm f/2.0 lens ($2,800) and the 20MP
Sony RX10 with the Carl Zeiss f/2.8 zoom lens ($1,000). You might also consider the 20MP
Panasonic FZ1000 with the Leica f/2.8-4.0 zoom lens ($800) , the 12MP
Panasonic FZ300 with the Leica f/2.8 zoom lens ($600), or the 16MP
Panasonic FZ200 with the Leica f/2.8 zoom lens ($400).
An interchangeable lens camera with similar capabilities might cost more, but it might not, and it would provide better results.