This question is best answered by your plastic surgeon, as each has his/her own preferences. As long as the cart or stroller isn't excessively heavy, you could proceed with this activity after approximately 7-10 days. Still it is is best to check with your surgeon as recovery is an individual endeavor.
There is no significant risk to pushing ga stroller, grocery cart after your surgery, unless it is uphill, and weighs 90#'s. DO not extend your arms too much to push the cart, keep them rather tucked and use your body to 'push' it with your arms as the fulcrum.Best.