The 10F series of microcontrollers from Microchip will work, as will almost any microcontroller (I can't think of one that won't). Overkill? I don't think so. It needs to both a timer and have a preset trigger based on the time. A 555 would probably be a more complicated way to do that. It is hard to compare prices, because so many options are available. At DigiKey for SMD components, the price for an LM555 is $1.03 and $0.39 for quantities of 1 and 3000, respectively. For a 10F200 MCU, the prices are $0.50 and $0.35 for both quantities, respectively.
Given such a vague description, I suspect this is not a Raytheon-size company's project, but is more likely wishful thinking by an individual. The list of suitable devices can be narrowed only with more information.
John