Crush the graham crackers in a small shallow dish. Add the sweetened condensed milk to a second shallow dish. Dip the rims of 2 glasses in the sweetened condensed milk to coat, then dip in the crushed graham crackers until evenly coated. Place the glasses in the freezer while you make the shake.
Combine the remaining sweetened condensed milk from the plate with the ice cream, whole milk and key lime juice in a blender (preferably high-power) and process until well blended, 30 seconds to 1 minute.
Divide the milkshake between the prepared glasses. Generously top each milkshake with whipped cream and serve immediately.