I expect they were twins once upon a time. Mine has my door number clumsily painted in white gloss on the side. Theirs has more accumulated filth in the bottom.
I'd just switch it now. Doing it in the night is weird. If they see you, just say, bin men mixed the bins up with a tut and a roll of the eyes. You're doing them a favour; nobody wants a mislabelled bin.
No. 2 sounds funny. Do that regardless.
What's so good about your bin compared to theirs?
Sounds like an episode of Curb.