We all settle on our own way of doing things, and that includes how you execute a dovetail joint.
With the outside of the tails cut, a coping saw is my first choice to remove the waste pins.
I cut the outside waste pins, just shy of the base line with a handsaw.
From here you pare to the baseline, halfway through the board, using chisels in incremental steps, flip and repeat from the otherside
Transferring the lines to the pin board is a feat with a table this size, quick clamps help to keep things in place.
Cutting the pins is more of the same, keep the chisels sharp and get out of the way of the saw.
Next Up, cutting the shelf joinery.