Is there a way of leveling a sloping floor without damaging the floorboards themselves?

it depends on what you want to achieve, if you are planning on placing the boards back down, then a slight amount of damage may occur in prizing them up due to nails being previously used to secure them, once this is done you can plant new timbers to the side of the existing floor joists to level the floor and then relay the boards,

The floor boards will be very dry which makes them easy to split. Making the boards damp or even wet will lesser the risk of splitting the boards trying to get them up. Wet floor boards will make them swell up so be sure to let them dry out properly and shrink back to the size they were before you put them back down.