If your gym has a power rack, you could set-up very low rack pulls. Example: https://www.youtube.com/watch?v=gkg3Rd4Vnls
The other option is do a deadlift, but don't touch the ground each rep.
Or start in a RDL position, but do a full deadlift range of motion, without touching the ground.
One way to help with this is rather than use 45lb plates on each side, use 25 lbers, so you have more room until you hit the ground. Example: https://www.youtube.com/watch?v=9rYbDx8vzao
That's one of the biggest differences with a RDL- in a deadlift, the eccentric (lowering) phase tends to not get worked as much as in a RDL, because people are often not as controlled, hence the noise when touching the ground. As you alluded to, "the weight drop."
If in either one you're in a conventional stance though, the differences are so minor they don't matter for most. If you were competing, then that ability to lift the bar from a dead start, at the bottom, really matters. When you're just trying to work some muscle, it's no big deal.
Hell, if building muscle is your goal, you can make an argument you want that extra eccentric work, which means RDLs have an advantage.
(I don't want to make this a concentric vs eccentric debate, but here is one study showing the benefits of eccentric training on quadricep hypertrophy.)
As an aside, my experience in gyms has been it's no so much deadlifting owners have a problem with, it's the attitude that too many end up have while doing them. If you're grunting where people 20 feet away can hear you, yelling, letting the weight free fall, that's where the problem comes in. But it's not like any of that is necessary.