Your dog can go for short lead walks from the evening of their neutering unless your vet advises otherwise.
Even toilet breaks should be on the lead if there is any risk that your dog will run or jump! Dogs are more relaxed and heal faster if allowed to go for short sniffy walks rather than if they are kept crated or in the house during recovery.
Gentle training such as scent work can also help occupy the brain during recovery. The skin wound will be healed in around 10 days, BUT full healing will take four to six weeks so exercise should be restricted for a minimum of four weeks. These guidelines apply to laparoscopic (keyhole) surgeries as well as more traditional techniques.