Do gases with high molar masses travel through small openings faster than gases with low molar masses?

I wouldn’t think so, unless you include a propellant. Sorta like with the aerosol can. I don’t expect mass to matter much unless you’re driving the gas gravitically.
All things being equal, I’d guess that you’re looking at the same rate of flow in both cases.

But then, I’m no physicist.

Actually, it’s the opposite. Higher molecular masses will pass through an opening slower, as they are generally larger and more dense. I suggest you take a gander at Graham’s Law of Effusion.

Thanks.

@BhacSsylan is correct. This effect was exploited for the isotopic separation of U-235 in form of uranium hexafloride vapor by the Manhattan Project at Oak Ridge Plant K-25.