All depends how yours is put together and without looking at it I can't tell you.Normally the string (the side) have two tenons into the newel post glue with two dowels on the internal post so you can do more damage specially with the tread and riser butted inside the newel post when taken apart.This is really a job for a experience carpenter with a staircase knowledge.The only other easiest way is to cut just above the string and use fastener bolt type to screw your new newel post + glue on top of exsisting one.
They are many type of fastener fixing,see this for some idea.
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