Appropriate tool to remove wires in push wire
I use one of the flat blade screwdrivers from this tool set from General. This is available from many better hardware stores or directly from the General Web Site. 



I have found that the flat ends on these are formed much longer and the poke down into the slot on the back of the outlet much better. The flats on the type of screw driver bits that you pictured generally get thicker within a much shorter length.

When you replace the outlets / switches with new ones do use the screws instead of the poke in wire holes. This will produce much more reliable connections. Another thing to watch for is to place the wire hook under the screw head so that the end of the hook goes around the screw in the same direction that you use to tighten the screws.