I see this is a little late for you, but I've found that the Above Reproach LTR will prevent accusations of cheating no matter how many romantic partners a sim has had. I've had a couple of sims whose only "hobby" was... ummm... let's go with *relationship building*, and no one ever objected. The only way to get "caught" is if the other sim literally walks in on the partner with someone else.
Also, if your sim is in the middle of a task, and the action "be accused of cheating" appears in the queue, it's possible to preempt the accusation before it fires. Just get another sim to try to talk to the would-be accuser, and the action gets dropped. But this only works if the supposed cheater is in doing something else and not just standing around waiting for the accuser to show up. It also might not work if the accuser is not a member of the active household, but then that sim can just be reset.
Oh, and if the cheating sim is asleep, the accuser is forced to drop the action and can move on. I've always liked how considerate sims can be towards each other. "I was going to scream at you and ruin your reputation with everyone you've ever known, but I'd hate to interrupt that great dream you're having. Sleep well, and I'll have forgotten all about your indescretions in the morning. But when you get home from work..." I guess the secretary's perfume really does seep into everything.