Stainless steel pusher with a rounded, spoon-shaped end. The Tweezerman Pushy is a good place to start. Metal horror stories come from people scraping at dry nails while holding the tool nearly vertical. Soften things first with a shower or a few minutes of cuticle remover, then hold the pusher at a low angle.
White specks from your glass one mean you’re pressing hard enough to damage the nail plate, and no tool should need that much force. Pretty Sure I Have Keratin Granulations The orangewood stick sliding over everything is normal. Metal will do more in ten seconds than the others manage at all.