No one likes feeling dumb.
Never underestimate the audience — they are smarter than you think, and they will get the joke.
One of my instructors, Cynthia Whitcomb, brings this up in every class, and every single time I’ve been unsure, I’ve run with it and sure enough, the audience does get the joke. Every time.
And, every time I didn’t run with it, and added “explanation” of the joke, when it finally showed to an audience, it fell flat.
It’s like punning. Punning only works if you let the audience know you’ve told a pun, and the typical reaction is not laughter, but groans. Avoid a groaning audience.
Not everyone will get the joke, but someone will and they’ll explain it. By dumbing it down or over-making the gag, the only thing that’s going to happen is that the people who had to have it explained are going to feel dumb and the people who caught it the first time are going to feel insulted.