It's from The Sands of Mars by Arthur C. Clarke. It's possible Heinlein wrote something similar, but this fits the description even down to the Station Director's wife popping up an an inopportune time:
"When you've been in space as long as I have," said Scott smugly, "you'll know what's wrong. There are plenty of handholds for you to grab in a ship like this. But suppose you want to go over to a blank wall at the other side of a room, and you launch yourself through the air from wherever you're standing. What happens? Well, you've got to break your fall somehow, usually with your hands, unless you can twist round on the way. Incidentally, do you know the commonest complaint a spaceship M.O. has to deal with? It's sprained wrists, and that's why. Anyway, even when you get to your target you'll bounce back unless you can grab hold of something. You might even get stranded in mid-air. I did that once in Space Station Three, in one of the big hangars. The nearest wall was fifteen metres away and I couldn't reach it."
"Couldn't you spit your way towards it?" said Gibson solemnly. "I thought that was the approved way out of the difficulty."
"You try it someday and see how far it gets you. Anyway, it's not hygienic. Do you know what I had to do? It was most embarrassing. I was only wearing shorts and vest, as usual, and I calculated that they had about a hundredth of my mass. If I could throw them away at thirty metres a second, I could reach the wall in about a minute."
"And did you?"
"Yes. But the Director was showing his wife round the Station that afternoon, so now you know why I'm reduced to earning my living on an old hulk like this, working my way from port to port when I'm not running a shady surgery down by the docks.
