I'm to create an orphan table (no relationships with any other table whatsoever) that contains 3 columns.
If col1 is your real primary key, there is no reason not to use it. Especially if the table is that tiny.
You would need to maintain a unique index on that column anyway, so by adding an artificial primary key you just add more overhead fon insert and delete operations (as two indexes must be maintained).
Unless you are referencing that PK from really, really many other rows (and other tables) you should just go with what is the natural primary for your business rules.