On a burner?....you know what a burner is, right?... to BURN it on a whim.
I'm not an IT guy, so I don't know how IPs work. but even so, a layman can understand that as long as your name isn't attached to anything on that phone you can toss it away without worrying about anyone 'tracking you'.
If you're really that paranoid, buy the burner phone and any 'pay-as-you-go' minute cards with cash, never credit or debit. IP of the phone or serial numbers of the minute-cards could be linked to the receipts stored in the store's computer. If "they" really wanted to get to you because you're an 'FBI top 10 suspect' that's how they could track you. But you're a poon-mongerer, not a terrorist. If it makes you feel better. Wear a hoodie and a COVID mask in the store, pay with cash, and hope the store doesn't use 4k CCTVs.
As for the hotel wifi, they don't use individual wifi routers in every room (maybe in 5-star VIP suites, I don't know). It's usually one per floor, or every few floors, depending on how strong the router is. Basically it'll be way too vague on who is using that router, anyone could use them with a password.
besides that, if you really feel the heat for being scared by a tough talking scammer, ditch your phone....done...