Is a battery management system necessary for wearables?
What exactly is needed will depend on how your device is marketed: in which countries you will sell it, will it be a certified medical device or not, etc. Specific requirements will apply in each case and it's too broad for an answer.

Also, most standards don't ask you to implement a particular feature such as BMS but to satisfy specific requirements. A good start would be the norm IEC 62133, which defines specific tests your battery should pass (mechanical damage, over-current, overcharge etc.). AFAIK this norm is used a lot for wearable batteries, but it might be insufficient or overly strict depending on what device you have exactly, as explained above.

AFAIK a simple wearable gadget with no medical functionality will be OK with a simple fuse for over-current protection. Some medical devices also get away with very simple chargers if the user is unable to charge the battery while wearing/using the device (e.g. electrical toothbrushes).