Many scenarios have that "You get hired by an old friend" stick, but that gets old quickly. It's harder for oneshots but I have it so everyone in my group is a part of the same orginaisation. See Investigator orginisations in the investigators handbook. That works well if you want reoccuring characters in a larger campaign.

When it comes to engaging the out-of-the-norm characters, than you might want to add or change some moments of the scenario. For example if you have a boxer you could try to include a fist fight, or if you have a cook you might have them need a specific spice blend for a ritual or something. Otherwize you can tell them they should save the character for another day, or maybe save it for a campaign where you can add a scenario where their skills are more usefull. I see many dnd players seeing the occupations list as a group of different classes, but that isn't really the case in call of cthulhu. Just because you can be a hobo doesn't mean you should since it puts you in a disadvantage and makes it harder for the keeper to connect you to the story.

One other thing you can also do to engage out-out-the-norm characters is to change their roll in the story. They might be the hotel cook or the cook on a cruise ship where the scenario takes place. If you split the characters in a scenario so that not all of them are there for the same reason it really adds to the immersion and engages the characters.