People aren't usually watching you as you make your introductions, they are usually doing their own if you are meeting another deal team/client team.
People don't realize as much as you give them credit for.
Naw, people are pretty perceptive. Plus, I'm not dealing with idiots - they can tell something's a bit off, especially if you're spending the next 1-3 hours with them at a meeting or dinner. If I used the "I have a cold" excuse, there's something wrong with me if I'm sick every third day of work.
Weren't you concerned with your client who never met a Jew before? Who cares if your team notices. A side discussion after the fact is not a awkward.
What's important is that you ask your lor, follow his guidance. So I have no qualms with what you do based on your psak. Just not something that I've been told/comfortable with.
I don't thing a conversation saying, "I can't shake your hand, but I'll shake hers so she has a favorable impression of Orthodox Jews" is a normal convo to have.
I'll agree to disagree, and it could be we work in different settings. I reiterate that when there's a reliable psak, I try to be as normal as possible.