Yes, you can solve that. If it's two corners swapped it's a possible scenario.
I solve this parity, if you can call it one, by turning 3 adjacent edges around their corner, always one after another in any direction. After 9 turns (twisting every of the 3 edges 3 times) you end up having 4 corners swapped. Move would be: [UR FR UF]x3 If you then just use your alg for swapping 3 corners you can solve it. Assuming you have an alg to swap 3 corners, which I think is the case since you almost entirely solved the puzzle except this "parity" case.
Now my method isn't really elegant or fast but it's easy to memorize.
If you want to speed solve, forget it, otherwise it does work.