1.  Herbal bath
This may be acceptable on ocasional basis.  Most confinement nannies or grandmothers taking care of you will know how to prepare such a steaming hot bath according to their own "recipe".  If not, you can probably purchase pre-packed packages from the Chinese Medical Halls for post-natal baths.  Alternatively, you can use products that have been formulated specially for this purpose.  Some stores like Little Dreamers carry a range of such organic products for these purposes.
 
 
 

2.  No-water cleansing
Try PhysiOBebe by Mustela..  You can buy this from most pharmacies or at Robinsons Dept Store.  It is a no rinse cleansing fluid that is linically proven mild. Enriched with aloe vera to hydrate and saponaria extract to dissolve dirt, this hypoallergenic fluid is light and truly refreshing!  My husband with his oily skin loves it for the convenience of cleaning his face during the day at work without the risk of wetting his best shirt & tie!
 
 

3. No-rinse Shampoo
For those with long hair especially, not washing the hair would be a torture.  Try a no-rinse shampoo to keep it clean.  There is a powder-like brand in the market that comes in a purple bottle.  Most pharmacies have it.  You can try NTUC pharmacy.  You can also try other brands like No-rinse Shampoo & Body Bath.