Yeah, it would have been considerably easier to keep that part-time job secret if nobody had known they have such a job. Now they have to reject describing the job, which is kind of suspicious. It could be at this point less suspicious to continue with a half-truth, telling what it is but leaving the whole crossdressing part out of it. It will still, nonetheless, lead to a situation where classmates would want to visit the restaurant just for the heck of it, even if they believed it was a more regular one. I guess they could instead lie about the whole nature of their job, making it something impossible for outsiders to observe or mess with, but I'm not sure if Yuuki is much of a liar. Plus they couldn't do it right there and now as they haven't agreed on any story.