If the OP wants to shower, he may do well do check out the RCC. I have used the London Lounge showers before, and they are subpar. I have not used the RCC showers, but I believe I read on FT that they are superior. I have no knowledge of whether showers exist in the SKL or, if they do, of their quality.

In any event, why not visit the RCC? At least the OP will have greater appreciation for the LL/SKL!