I'd personally go airside, transit via uk connections, and Galleries lounge which is a bit more pleasant and much closer to both the arrival from the main transit security route (the escalator one) and the domestic gates. Showers should be no issue either directly or, as cws pointed out, after a short wait with beeper.

Every other alternative would complicate their lives a little or a lot for little to no benefit depending on case. None is worth it.