Assuming your razor is sharp enough and you have prepped properly, perhaps try using different parts of the blade. For just under the nose I find the heel of the blade is very controllable, the toe for the sides and edges. Keep the blade flatter than you normally would (i.e. less than 30 deg). And stretch the skin.

You're right to use a light touch. Any pressure and you will get weepers. Let us know how it goes with the suggestions.