Just to elaborate a bit....
You could leave the outside paint on, maybe it'll flake off, maybe it won't. In my experience it will.
Plus the non-high temp paint might release fumes when it's heated, then it again maybe it won't. Remember it wasn't originally intended to be heated up a few hundred degrees.
Rattle can with high temp. Then there will be no peeling issues. There'll be no possible health issues. Plus a uds just looks right flat black!
UDS, mini wsm, 22.5" weber kettle