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If you are really worried about the battery then get a battery charger and every month or so top off the battery, it's good for the battery to get fully charged every once in a while even with normal driving.
But to the root of your question, I don't think restarting in the middle of a 15 minute trip is going to shorten your battery life much, think of all of the delivery drivers who restart their cars every 3 minutes or the people who only drive 5 minute trips, my trip to work is about 10 minutes and I shut my engine off mid way and my battery is nearing 5 years old, twice a year I top it off with a charger just to make sure it's full and healthy and I don't have any issues with it starting on the coldest winter mornings.
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