Mains or battery shaver does not matter, they can both cause interference.
To answer the original question, wrapping the shaver in aluminium foil is not a reliable means of reducing intterference. This is mainly because it will not provide reliable contact, even with itself. It might even form a resonator making emission worse for specific frequencies or directions. Covering the razor with self adhesive copper foil, soldering all the seams and providing a ground connection would probably help, but without making measurements you cannot be sure.
An isssue with modern implantable medical devices is that many have a "remote control" capability sometimes with an antenna remote from the device. This makes them more vunerable to interference.
This is a classic case of safety probability / impact assessment. The probability of emissions causing problem is low (probably "extremly remote,10-7 in safety terms) but the effect is catastrophic (death) so additional precautions, keep emitters away from device) are required to bring the probabilty dowm to an acceptable level (<10-9).
Note that on another threads on VFDs I have commented on the need to fit proper EM/EMC filters. Your device is one reason for this so please take care aroung machines with electronic speed controls particuarly DIY set-ups.
Note that the interference drops with the square of the distance, doubling the distance reduces interference by 4, so knowing were the device an any antenna are would allow for a better judgement to be made. If they are in the neck/head then electric shaving is a no-no, if they are in the abomen then you could make a judgment call.
As a professional engineer involved in EMI/EMC I can only recommend you follow the advice given by the device manufacturer and your medical specialists.
Robert G8RPI.