My answer covers the meaning of this expression, including its social connotations. How to express the in English is off-topic on this site, and there isn't enough context in the question anyway.
“Please have him receive my cordial handshake” is a correct literal translation. In other words, “please shake his hand on my behalf”. The cultural implication is “...
Suggestion from Gilles Thésée:
“kilomètres par la route”, as opposed to “kilomètres à vol d’oiseau” (“as the crow flies”)
https://www.google.com/search?q=%22kilom%C3%A8tres+par+la+route%22 does return a few results (but not that many).
"Kilomètres de route" is completely correct. As a native French speaker, I use it on a daily basis.
We tend to consider it the normal way to express a distance though, and so usually omit it. The opposite being "kilomètres à vol d'oiseau", is also frequently used.
The expression km de route does exist in French and Google finds many occurences but Chaiyaphum est à 337 km de route au nord-est de Bangkok is not something I would expect to hear from a native French speaker. What would be more common is: Il y a 337 km de route pour aller de Bangkok à Chaiyaphum but it is difficult to place northeast in this sentence.
"Mignon" is the translation for "Cute", but cuteness doesn't really have one.
You can either use made up words like "Mignonnerie".
Or you can say that it is cute. "C'est mignon." "C'est trop chou !"
But it might be different from what you need depending on the context in which you want to use this. Did you ...