It might be worth updating to a more recent compact or micro 4/3rds. Even the biggest m43 camera isn't going to be much bigger than your C750.
Most compacts and m43 cameras have a scene mode which will blur backgrounds, miniaturisation mode ( great fun this one) and others for almost every occasion.
Your not really gong to get a proper out of focus background with your camera, after all, it must be almost 10 years old by now and technology has moved on somewhat.....
Allan