Oddly enough yes Helium has a smaller atomic radius because the additional proton and electron complete that first electron shell and get pulled closer to the nucleus.

Helium is a strange bird. Every other element in liquid form will freeze if you drop the temperature enough, except Helium. You must greatly pressurize Helium for it to freeze. It is worth pointing out that while the atomic radius of Helium is smaller than Hydrogen, Helium is still the heavier element. It’s small radius and tendency to remain a gas or liquid makes it very useful in testing for leaks or as a purging gas.

Hydrogen is mighty weird too.

For leak testing, it can be better than helium because the molecule is lighter. This raises the speed for any given temperature, and thus increases the rates of diffusion and effusion.

A downside is that hydrogen can burrow right into solid metal, one atom (proton) at a time, and then merge back into diatomic molecules. This creates a sort of internal pressure in the material, making it brittle. Hydrogen embrittlement is a significant problem, particularly with titanium.

That's an understatement. Helium cooled below 2K loses literally all viscosity and will flow through porcelain like it's a sponge. Not only that, because there's literally zero viscosity, convection makes superfluid helium a great heat conductor. All of this was discovered back in the 30s. The man who discovered superfluid liquid helium must have truly thought he had gone insane.

Also, atomic Hydrogen is not very common around here (nor anywhere, I suppose)... H+ and H2, on the other hand...

Well, I'm not a physicist, but hydrogen gas is two atoms compared to 1 atom for helium gas.

  hydrogen gas is two atoms

... which makes it a molecule.

If you belive Wikipedia https://en.wikipedia.org/wiki/Atomic_radius then the atomic radius of Helium has never been measured, but it is predicted to be smaller than Hydrogen.

A google search says yes.