Mezuzah on hotel entrance doorpost? Research question

Hello, first post! I’m a Jewish writer and this is a very specific historical research question for a novel I’m working on. I’m finding vague answers and wondering if anyone here might have some wisdom.

I know hotels are exempt from having a mezuzah on a doorpost, but I’m wondering: Is it still likely—or simply at all possible—that a Borscht Belt hotel in the Catskills might have had one on an outer door? (Not on the rooms themselves but on the front door to the whole hotel.) Anyone have any knowledge of this? If that’s not not likely, I need to cut something from the book so I’m trying to fact-check to see if it’s possible! Thank you in advance if you can offer some help or research guidance.