Am electrician and live in a double-wide so I haven’t tinkered with it beyond swapping some devices. Feels good to be able to just do stuff like this, as simple as it is. I was not raised to be very handy so learning all this has been a deliberate process.
Uh, this doesn’t count as a legal, professional consultation and you should always seek a licensed professional when it comes to electricity in your home.
I’d put it in some conduit if I were you. 1/2" PVC is fine for a single cable and braindead easy to run. Technically if it’s exposed it should be schedule 80 but you can get by with 40. Any protection is better than none.
Flexible conduit is an option too