It's very stiff and buttoned-up, or buttoned-down, whichever. Walt sounds more old-mannish than Walter, like someone's slightly crotchety grandfather. Wally sounds like a dimwit.
I would not use Walter with a last name similar to Parker. It just sounds too Foghorn Leghorn.
The Walter the Farting Dog series for kids is pretty popular still. God alone knows why.
Before you criticize a man, walk a mile in his shoes. That way, when you criticize him, you're a mile away and you have his shoes!
Steve Martin