Even with these precautions, I got poked with a glass sliver. For me, it worked best to give the broken glass a blanket of duct tape to control loose pieces of glass. Taping both sides is smart to keep all glass slivers adhered. I used a rubber mallet's flat striking edge rather than a hammer to fracture the remaining window surface, then lifted away the duct tape, with most of the glass coming along for the ride. To pluck the shards stubbornly sticking in the frame, I used needle nose pliers as grabbers and ran a single pliers tip through the frame afterward to catch any stray nuggets.
Some people use a screwdriver or awl to slide through the frame.
Others heat the old putty with a heat gun or hair dryer to soften it and free it up, but my project had the pane held in with wooden molding and only a trace of old putty. Two coats of paint, aged over 57 winters, had shellacked the molding in place, so I split the seam with a razor blade, pried loose the four sides of molding with the flat tip of a putty knife, then scraped the bare wood. Putting the molding back on will be easier if you mark the pieces top, left, bottom and right as they're taken off. The odds were 50-50, but I didn't want to gamble with glass. I decided he was the right person to consult.