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First thing to recommend assessing is how easy it is to get up onto the exterior roof to clean your skylight. If there's any chance it is unsafe for you to be up there, call a professional window washer. It's not worth the risk for the sake of cleaning bird droppings.

It's recommended that skylights are cleaned twice a year to prevent residual dirt/rain/poop buildup from accumulating and ruining the clear view. Plexiglas skylights are especially prone to becoming scratched from minute amounts of dirt or any other abrasive material (and remember, birds intentionally eat small pebbles to aid in their digestion, so they're droppings are especially abrasive). Prior to spraying, inspect whether there are problem spots, and use a diluted citrus based cleaner to remove droppings or sap (test on plexi before using to make sure it doesn't haze/ruin the clarity of the material). We also recommend using a spray hose made especially for washing windows, set at a light mist to spray, then lightly soaping, misting rinse clean and then using a rubber squeegee readily available at any automotive parts supply store (these are soft rubber that prevent most scratches).