Yes, throat, belly, sanitary area (I only strip the butt), inside of back legs are all sensitive. I just take it slow and use a stone rather than a knife, or do it by hand only. As a puppy he freaked out a lot more, these days I can usually just lay him on his side and work on him that way.
FYI, I bathe right after stripping if I'm done and not pulling more the next day. And I typically bathe every 1-2 weeks, since we live in the city, walk miles every day, and Dax is so low to the ground. I routinely get compliments on his coat by conformation judges and breeders, so I'm not bothered when "old school" terrier folks tell me I shouldn't bathe him so much.