Sounds to me what you're looking for is simply some Thayer's Brand Witch Hazel. It's alcohol free, so it won't dry. It has glycerin and other goodies which will lightly moisturize your skin without being greasy/oily. And the witch hazel will tone & brace your skin, giving you that after-the-shave finishing, kinda feel it sounds like your looking for.
You can get it at General Nutrition Center retail stores, Adkins Health Food Store, Whole Foods, Sprouts or Natural Grocers. It comes in Peach, Rose, Cucumber, Lavender & Lemon, which all are very mild scents without heavy fragrance oils. Just the botanicals that you described.
Thayer's have a Superhazel Aftershave also, but it has alcohol added.
Recommend a Light Moisturizer for Oily / Combination skin?