Your plum patent wingtips have what we refer to as a 'natural edge' The color you see is the natural layers of the leather outsole with a clear finish coat applied before they leave the factory. The leather has a natural brown color so the liquid brown wax should be fine.
If you want to keep the 'layered' look, you will want to stick with a clear polish, paste or cream. Wax is used at cobbler/ shoe repair shops, but this is more of an industrial solution (there is a mounted wax block and the shoe edge is run along this block to seal any scuffs or scratches before additional polishing is done.
I have looked around online and if you are opting for home care (using the old elbow grease method), you can stick with a clear polish, paste or cream. Apply with a soft cloth or rag. This would be the desired solution while the edges remain in good shape and free of scratches.
If you find that the edges get scuffed or scratched over time, you will probably want to use a light coat of either brown or black polish, paste or cream (depending on which matches your shoe) to hide any surface imperfections.
There is never any substitute for professional shoe care Treat your shoes with a visit to your local cobbler/ shoe care service every once in a while and that should significantly extend the life of your shoes.
Hope this helps.