You can do RC4 on pen and paper, more precisely 256 pieces of paper. There’s also a variant of this cipher that uses deck of cards instead, RC4-52. There’s also another stream cipher that uses deck of cards to store state and it’s called Pontifex/Solitaire. Both have some weaknesses

VIC has way too short key for modern uses, but maybe there’s a way to strenghten it

On related note, i guess that it would be possible to implement modern stream cipher with NLFSR in electromechanical machine, no silicon needed. WW2 era cryptography like this (enigma, M209 etc) were in a way stream ciphers and these require some of least hardware. Key storage and scheduling becomes bigger problem