Is it possible to do some quests to get that guy at the front desk to quit requesting my weapons every time I walk into the place?

All casions ask for your weapons. If you talk to swank in the tops, he is at the main desk. You tell him about Benny, show him some evidence of what he did to you, he will let you go search his room after passing speech checks up to 45 speech. And he will give you your weapons back. As long as you only take out Benny, you can walk in and out of there with your weapons each time afterwords. Won't be the same for other casions though.

Do you mean casinos?

Do really think he could have meant anything BUT casinos? Or do you think casions is what they call people who pat you down and take you guns in New Vegas?

I think he meant that post as a lighthearted jokish correction of spelling. Don't take it so serious.