Solid wire has ever so slightly more cross sectional area than the equivalent multi strand wire since it does not have the miniscule air gaps in between the individual strands, and hence is capable of carrying slightly more current.
The downside however is that it is not flexible.
So, it IS ok to use solid wire in areas which will NOT be subject to any motion or vibration.
As far as the skin effect is concerned, at those frequencies and the lengths of wire involved, the effect is negligible and will be inaudible, especially if you use thicker than required wire.