I use a mild, for sensitive skin soap for all over my body, including undercarriage. I totally agree with indy, that stronger soaps upset the ph balance of your vagina and around there. Hotels don't necessarily offer great soaps.
Besides, you don't want to over-dry the whole undercarriage skin area with strong soaps.
In addition to strong sunblocks, is to generously use rich body lotion each time after shower. Even if one sweats alot during the day. My skin on my legs, etc. gets drier. (when already I have dry leg skin)
Of course, face moisturizer after shower is important since one is cycling for several hrs. daily.
I've only had the luxury of a sag wagon...3-4 group rides in all 20 years. Other trips I've had to cycle with my toiletries and clothing.
For long touring rides of severals or weeks, I make sure I have my hair cut short..so I don't have to use a hair blower!