Propose a method to find the specific heat of sodium which reacts with water

Two methods to think about.
Use a liquid with which Na doesn't react.

OR, use a weighed amount of Na metal to react with water. Measure T of the water before addition of Na and after adding Na. That will give you q and you know all the other variables. Great care would need to be taken to avoid explosive reactions AND to avoid spattering.

Check my thinking on that last one; that may only give you the delta H for the reaction of Na to NaOH + H2.