The only density that you need is the density of the mixture. You can express the amounts of liquids needed to prepare the solution as masses, and that'll be an exact answer.
If you don't know the density of the mixture you have to look for an approximation. Unfortunately, volumes are not additive, so it is not possible to precisely calculate the density of the mixture, even if you know densities of the components. However, in most cases errors introduced by assuming volumes ARE additive are small enough to be negligible (especially when you are aiming at a solution that is 1 m, and not 1.0000 m).