Is it possible to perform a rudimentary asymmetric key encryption algorithm by hand?
Yes, you can perform rudimentary asymmetric encryption or signing by hand, but no it won't be secure.

Textbook RSA with small enough numbers is easy to do by hand. Diffie-Hellman to exchange a symmetric key is even easier. However, the kinds of numbers for which this is feasible are far from those needed for real security.

There are a lot of other asymmetric systems, but those tend to use even more complicated (to humans) math. Generally asymmetric encryption on a computer is something like an order of magnitude slower than symmetric and like the question you linked shows even secure symmetric encryption is barely doable, maybe, by hand.