All those good points been said and noted; I say go for it if you think it is important. A 21-day cleanse is good with or without Reiki.
The term "cleanse" is misleading in a way. If done in a respectful (to your body) way it will be cleansing and purging and in the end, healing.
But keep in mind it can be quite challenging on two fronts. During this one is releasing both toxins and negative thought forms/patterns locked within. That can make for a ruff ride; moreso psychologically. Emotional / interpersonal 'crap' is likely to get stirred up from within to some degree affecting mood and demeanor.
But if you keep aware of that potential dynamic...well knowledge is power as they say.
Namaste,
Michael