I had the exact same issue with a boom arm I bought which didn't come with the adapter either. I just bought a separate adapter and it works like a charm.

I don't use a shock mount on it, though, so I guess your mileage may vary.

can you list what you currently have? it sounds like: -5/8' female on the arm. -3/8' male on the yeti -adapter of some kind

yes?

this usually works for stepping down: https://www.amazon.com/Stage-MA-300-Female-Knurled-Adapter/dp/B001H5KP0M/ref=sr_1_6?crid=2IMLANA9K71BT&keywords=5%2F8+adapter+microphone&qid=1578932863&sprefix=5%2F8+adapter%2Caps%2C186&sr=8-6