Would this be safe for me to do?
Short version : No.
Long version : That is a jocular article written in the pre-Xmas season. Some medical journals have a tradition of accepting amusing articles written half (or maybe 90 %, as in this case) in jest in their holiday season issue.
The preferred method of removing cerumen IS with syringing (after softening with oil), but it's better to let a professional do it with professional equipment. A low pressure jet must be used and it must not be directed straight at the tympanic membrane (TM) (aka the eardrum), or you'll perforate it. It should aim to gradually dislodge and suspend with lots of water at lower pressure directed obliquely at the walls rather than to blast anything with high pressure out of your external acoustic meatus.
So go see a doctor about cerumen, and give your kid/nephew back his toy.
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