See Active matter, Microhydrodynamics, and Kinematic reversibility in fluid dynamics for more
Zero reynolds number doesnt mean no acceleration. It just means that no force is needed to cause that acceleration
In the zero Re limit, if the swimmer accelerates (say by varying the velociy of the corkscrew), and if it has a finite mass, the fluid will exert a net force on the swimmer, and thus the swimmer will exert a net force on the fluid, momentarily creating a Stokelet component. If we somehow had a small but very heavy swimmer with a large thrust too, it would then create a Stokelet velocity field for a significant period of time.
Happel and Brenner book: Low Reynolds number hydrodynamics (book)
Reciprocal theorem
The reciprocal theorem allows one to determine results for one Stokes-flow field based upon the solution of another Stokes flow in the same geometry, i.e. having the same boundaries but different boundary conditions.
See A physical introduction to suspension dynamics.