I came up with a similar but not exactly the same approach in which i just counted mismatches and thought to apply some function on mismatches that would directly give swaps:

if mismatches%2:
    return mismatches//2 + 1
else:
    return mismatches//2

But it somehow fails test case 1, 2, 3, 6. In the end I decided to go with actually swapping and counting it

Isn't there any such function that could direcly be applied on mismatch count to yield number of swaps?