If you have numbness under the arm (likely with axillary surgery) you will probably not be able to distinguish hot and cold very well. So I would stay away from hot wax until some of the senses return. The major issue with lymphoedema is the risk of infection if you get a cut or wound to the affected part. If you don't have lymphoedema, I doubt if shaving will cause it, but cream may be safer all round. Regarding a prosthesis, the fitter will probably have preferred makes. Most frequent swimmers get a prosthesis especially for swimming. I don't swim a lot and have used a synthetic pad quite happily on holiday. For a small cup, you may very well be able to make a pocket in the breast section of your preferred swimwear, modelled on a prosthesis bra. Best wishes.