I don't see a problem with having your bird on your shoulder if its well trained and good behaved and as for the bird sliping I always tend to wear clothes that the bird can get a firm grip of to prevent it from sliping
The supermarket is one of the scariest places to be for a bird that would normally never leave the house. Everything is designed to be bright and attract your attention, it can be overwhelming to some parrots - but Piki did really well!Perched quite happily on my shoulder was Piki. Forgetting he was there I travelled throughout the town unaware of my passenger.