"but does so" is correct and usable in written English.
You can use it to express contrast between two ideas. For example: "He is not able to articulate his thoughts clearly, but does so confidently."
Burton satirises his characters but does so with affection.
The computer does the actual animation, but does so according to the operator's instructions.
She hasn't especially revisited the territory since, but does so in her new film, Bad Teacher.
Link's second collection has a McSweeney's-like tendency to digress, but does so without irony.
It punishes a perpetrator, but does so with a sentence that can't be undone.
It administers all of these hard truths, but does so matter-of-factly.
Or the college seems to meet the need but does so with a large portion of loans and campus jobs.
Recalling Albrecht in "Giselle," Mr. Baryshnikov strews lilies on the floor but does so while rolling back in his chair.
The other also has a box to lean on, but does so with less sense of virile assurance.
Galileo is not prepared to recant to save his daughter's marriage but does so to save his own skin.
Such laments are common in the party that once dominated American politics but does so no longer.
