Yes you can walk across the Williamsburg Bridge.
The Williamsburg Bridge has a pedestrian walkway for people to walk across the Williamsburg Bridge safely.
Cyclists also bike across the Williamsburg Bridge on the walking pathway on the bridge as well so just be careful if you do walk across the Williamsburg Bridge.
Watch out for cyclists who sometimes ride really fast across the Williamsburg Bridge and you'll be fine.
The last time I was in New York I did walk across the Williamsburg Bridge just because I wanted to walk across it and take my time.
I was just there visiting and wanted to enjoy the sights.