Interesting read.
As shluchim, my husband and I encounter this all the time. This is not the business world but often the stakes are just as high - meeting a potential big donor. Meeting politicians in high places, meeting people who have enough friends that on their recommendation your attendance at Hebrew school can be doubled, meeting members of the zoning board and so on.
What we try to do is explain concisely why we don't shake, and making a point to smile, be friendly and to kind of "lean in". meaning sometimes u subconsciously lean back or take a step back -so I make sure not to.
My husband used to say something along the lines of my wife gets jealous but I told him that people don't get that's its a jokeand it makes me look pathetic.
If we are both together, my husband will usually them the man, "but I will shake your hand twice"
Yes it often times makes them uncomfortable, they usually apologize and I feel bad but is also is uncomfortable when someone brings flowers and I leave it on the counter without putting it in water.
Or when someone brings food or wine for the meal and we don't serve it and the list goes on. ..
For us it's halacha and we try to make it as smooth as possible.