Do I need to replace skirting in these places?
Nope -- cross that task off your list!

Seriously, skirting boards (aka baseboard or baseboards to feed the search engine) are cosmetic. If you can't see them, you don't need them. They'll get in the way when you're trying to push the dishwasher back that last little bit.

(Some people think they keep creatures out... the simple fact is that if you have creatures and they want into your space, they'll find a way.)