Can you put shock in my pool skimmer?

Yes - everybody says not to, but everybody does it. Just add it slowly so that it actually goes through the basket and doesn't just glom together.
"Everybody" doing it is no excuse for bad practice - it only shows the "everybody" you know does not respect their costly property, nor really understands it. The equipment manufacturers tell you not to add chemicals via the skimmer (apart from some flocculants) because it creates unfairly strong hence potentially damaging concentrations, albeit for short times but oft-repeated, in the plant. Follow the instructions supplied with the chemicals and the plant - they are written by people who know rather more about the subject than your "everybody".