You can be amazed of its density, but that is safer to do with the lighter, but much cheaper, tungsten.
Most chemical elements with atomic numbers equal or greater than that of lutetium are very slightly radioactive (with a few exceptions like iridium, gold, mercury and lead). Rhenium is one of the most radioactive of them, but it is several orders of magnitude less radioactive than thorium and uranium.
Nevertheless, its radioactivity is so weak that it can be handled safely with bare hands. Even so, making some jewelry kept permanently on the skin is unlikely to be a good idea.
> Rhenium is one of the most radioactive of them, but it is several orders of magnitude less radioactive than thorium and uranium.
Rhenium does have one stable isotope, which comprises 37,4% of naturally ocurring Rhenium. 62,6% is radioactive Rh-187 with a half-life of 10^10 years. That's a bit longer than U-235 or U-238.
But unlike uranium, Rh-187 decays into stable osmium.
Yeah, rhenium radioactivity is pretty much irrelevant for health.
I would worry more about radioactivity as a failure mode for these transistors. Given how fast these are and how few atoms are supposed to be there, the question is if a single atom in the lattice undergoing fission can
a) blow up the lattice enough to disrupt it
b) make it no longer perform the function because the atom that is there has different chemical properties
