Nope! Not gonna do it. I'm putting my foot down on this one. I really have to wonder if I'm the only one in the world who's bothered by this. I don't see anyone else getting annoyed when this happens. I'm not a mediator or a translator for you. So when I'm talking on the phone I don't want to be a go between for you and whoever I'm talking to.
I find it extremely annoying when I'm in mid conversation with someone and someone else in the room decides to say "tell them I say hi". So now, not only am I distracted from my conversation, I also have to interrupt the party on the other end to relay your all important message. Then wait for them to say (awkwardly) "oh that's nice. Tell them we say hi also". No kidding. What else were you going to say? So, then I have to hold the phone away and transfer this highly anticipated response back to you..."they say hi back".
I'm going to suggest you use your fingers to dial their number and say hi yourself. While your still able. Because the next time you do this to me, you're going to discover that all of your dialing fingers are, how do you say??... Broken.