I know your talking about an Expo camper in the woods, but for the past five years I've used the common wheel claw lock, basic hitch lock and wheel chain with padlock on our event trailer all over the US. Now, the vast majority of the time the trailer is at an event so the likelihood of someone nicking it is low, but there is a number of times it's been left in NP's, hotels or offsite locations with this combination and no problems. While my confidence level is relativity low regarding these locks, particularly with a determined thief with a set of battery powered DeWalt cut-off tools and crappy truck, we haven't been a victim yet....(knock on wood). Also, statistically you're more likely to be a victim of trailer theft in your own driveway or in the parking lot of a hotel, so a good hitch lock system attached to your vehicle would be a good start. Good luck!
One of the more sleepless nights regarding traveling with a trailer...….I had to spend the night in a roadside motel while bringing my tractor home to the mountains. Knowing the risk associated with heavy equipment theft from hotel parking lots I backed the trailer up to the curb and a tree. Used two logging chains an four padlocks, wheel clamp lock, hitch lock, hitch chain locks and removed the starter and fuel relays from by ole Chevy, plus got a room that "overwatched" the setup......my poor wife didn't get much sleep cause I was up and down all night! So glad when morning came.