Okay, I don't know anything about the book you mentioned, so I'm not sure how close my recommendations (... such as they are) will be to what you want. But in terms of no-sex Regencies...
There is a whole genre devoted to no-sex regencies. Most of the Regencies you see these days are called Historical Regencies, and they typically involve some amount of sex. There is another, somewhat less omnipresent type of romance called Traditional Regencies, which to my knowledge, often have little to no sex. It's possible that searching for these would give you something to read?
Off the top of my head... Meg Cabot's written a pair of Regencies without sex in them- Nicola and the Viscount
and Victoria and the Rogue
. Any book written by Georgette Heyer would qualify too- but those are older books, and the language itself is a little different from most of the books I come across these days.
I'm sure there are more, but these are the only things I can remember right now.
Hope it helps?