What is wrong with "Teníamos que usar cascos de protección" . I have heard many people use "usar" for to wear.
Freeform Writing Exercise A2
It would be very similar, but the translation in English is saying "wear" not "use", that's all.
It might be that "usar" is used for wear more often in Latin America, but not in Peninsular Spanish
For me "wear" is a valid translation of "usar" in the right context
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