I am just limiting my answer to tools used in the First World War, because i am not aware (and propably do not know enough) about tools being used in World War 2 on a bigger scale.

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However, regarding the Great War it is important to note that none of the major powers aspected the war to become a stalemate with trench warfare. In the decades leading up to the Great war technological advancements enabled soldiers to reload their weapons faster and shoot on a higher range. Further artillery provided such massive firepower on a long range that it was not possible to charge with infantry and bayonettes like for example in the Napoleonic era. Thus resulting in bayonettes or sabers nearly not beeing produced (at least for infantry units cavalry still used sabers however cavalary did not play any significant part in the western front during World War 1).

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So soldiers had barely any equipment for close range fighting at the start of the war.

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After the first few weeks/early months of the war the strategy on the western front was to dig trenches (as menioned in your quote). Shovels were needed to build those trenches. If one army attacked the enemy trenches and were able to enter the trench itself, guns and rifles were nearly useless. As you can probably imagine aiming and shooting in small trenches is difficult and you are even very likely to hit your own troops. Further reloading with an enemy standing next to you is difficult and dangerous. So you were basically forced to enter melee confrontation. With the limited amount of melee weapons shovels were maybe the best melee weapons you could find in the trenches for the following reasons:

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• they did not need to be produced seperately
• they were already in those trenches or you carry them with you anyway.
• and shovels also have a much longer range then for example knifes.

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So even though it is impossible to know the eaxct numbers your quote that shovels have the highest kills once it comes to fighting inside a trench is very possible. However most troops died even before they were able to enter the trench through artilley, machine gun fire or regular rifles (thus do not count as killed in a trench itself).

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It should be said, that developments during the war like flamethrowers or shotguns made tools like shovels less important as a weapon in later stages of the war.

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I hope this post helps to solve your question. This was my first post in this subreddit so i do hope it fits the requirements for replying.