Cut papayas into 1/4-inch-thick slices and arrange on a platter.
In a 6- to 8-inch frying pan over low heat, stir ground cumin, cayenne, ground nutmeg, and pepper until the spices are fragrant, about 3 minutes. Remove the pan from heat.
Sprinkle papaya slices evenly with spice mixture and lightly with salt. Squeeze lime over papayas.