Variegated standard holly tree

My dad has a variegated standard holly tree in thier garden, it's a golden king variety. It needs pruning now as it's grown quite large, say 10ft high with a canopy spread of 8ft and has grown to large for the space now, the canopy starts about 4 ft up the main trunk. Looking under the canopy there are a number of crisscrossed branches some are quite thick, how and when can I prune it so I can reduce the spread of the canopy by half, if I cut to far back into the canopy where no leaves are will it kill the tree off as the leaves only go about 2 ft in. I've read on the gardeners world page it can be pruned in March. So as long as I cut out the dead, damaged, deceased branches and disorderly branches just after a node will it be ok, obviously the tree will be bare of leaves then.
Cheers An Gon
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Woukd I need to use any products on the larger branches where I prune to heal where I've pruned
Gardening in Central Norfolk on improved gritty moraine over chalk ... free-draining.