That's a wee jump if you're in a hurry, I suppose. I've never gone down to the States to work. Seems every time I think about it, something happens and border security goes nuts for a while.
If I do then I'll rejoin the Union. They're good at handling the paperwork. It has occurred to me though that I'd make no record of such an event on a web calendar.
Don't over-think this one. People carry instruments back and forth all of the time. The only trouble I've had was in London. Funny that!