the best time to switch is when the child is ready...sounds like your child is ready to give it a try. My son was drinking from a regular cup at age 2...but we didn't ditch the sippy, he still has a sippy in the car, the living room, on the go, etc...but at the breakfast, lunch and dinner table he uses a regular cup. You don't have to get rid of one to use the other. You can use both. :)
Once my son started showing interest, I would give him a cup in the bath and he would practice, yeah it's bath water and yeah it probably has pee in it, but honestly it's not the worst thing he'll digest in his time of exploring life. ;) I would fill the cup from the tap, but a fair share of scooped up drinks made their way. It's a perfect place to 'practice' that and the outdoor kiddy pool if warm enough. :)