When I was dating a young woman in my distant past we hit upon the same problem. It offended our sensibilities to say, "Let's fuck" or "I want you." We sat down and talked it out, sharing (verbally) our desire for freaky monkey sex without the freak or the monkey. What to do?

So, we came up with a catch-word. For us, the catch-word was "pink elephants." We decided to make the catch word something that could be used in the presence of any form of company, but would be so absurd that to hear it would cue the hearer in on what was really desired. So let's say the both of us are at dinner with our parents (all four of 'em) and we give each other that smothering "come hither" gaze. She might say, as she's talking to her mom:

"So I was sitting there and talking with Francis about this new dress she got the other day. Absolutely horrid, Mom. The thing had pink elephants patterned all over it. Pink elephants! Can you imagine?"

To which her mother might say, "Oh dear." And she would never be the wiser, but I certainly would know what's on my girl's mind. She has just told me that she wants me to take her away someplace soon and do the nasty while at the same time being a perfect lady about it.

bow-chica-bow-bow! (insert tacky 70's porno music here and segue into sleazy, meaningless, rauchy sub-plot involving flimsy hotel room walls)
Much boinkage will ensue.

We tried it. It works. Lots.

Use whatever phrase suits you best, but I suggest that you make it something not too outlandish. In our case, we had to change it up every now and then, lest our family members started to worry about a pink elephant fetish.