All this fuss for a simple job under the hand rail their is a piece of timber called a fillet its a slim bit of wood that sets the distance from one spindle to another you, would have to split the fillit to remove it. once the fillet is removed you can then just tap the top of the spindle towards the next spindle if the spindle does not move easy take a hack saw and gently cut through the holding pin or nail. remember your acting in reverse, that is to say when you remove you always remove top part of the spindle first then bottom start with the lowest spindle first then work your way up the staircase do not damage the spindles as you will need them to make new templates for the replacement ones. Go to any Timber yard for your replacement fillit timber which is sold in lengths which you cut to size.
always use a hack saw to remove any nails. The bannister (thing at the bottom do not remove this at any cost) the hand rail start at the top use a hack saw and raise the hand rail up slightly as it will have a socket fix to the banister at the bottom there is a pin in the banister you will have to drill this pin out to remove the handrail from the socket. So remember never remove the bannister thats the post at the bottom of the staircase when removing the spindles start at the lowest point and work up the stairs removing the top part of each spindle first then the bottom repeat on each spindle until you reach the top of the stairs when you reach your last spindle you are then ready to remove the hand rail start by hack sawing through at the top of the stairs as the hand rail will fit into a socket at the bottom of the stairs you will have to drill out the pin at the bottom banister as the hand rail is socketed into the bannister.
My brother was a carpenter for many years and I often watched him make beautifull staircases! *lol* seemed so simple! to watch anyway ROFL! http://www.diynot.com/pages/fs/fs023.php#a5
with pictures belowhttp://www.woodsthebest.com/Stairs/wood-stairs-railings.htm