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In this article we partially implement the program outlined in the previouspaper of the authors [A. V. Aminova and P. I. Chumarov, Phys. Rev. D 88, 044005(2013)]. The program owes its origins to the following comment in paper [M.Cveti\v{c} and D. Youm, Nucl. Phys. B, 438, 182 (1995), Addendum-ibid. 449,146(1995)], where a class of static spherically symmetric solutions in$(4+n)$-dimensional Kaluza--Klein theory was studied: "...We suspect that thesame thing [as for spherical symmetry] will happen for axially symmetricstationary configurations, but it remains to be proven". We study the radialand non-radial motion of test particles in the cylindrically symmetricwormholes found in the authors'paper of type $\rm WhCR^e$ in 6-dimensionalreduced Kaluza--Klein theory with Abelian gauge field and two dilaton fields,with particular attention to the extent to which the wormhole is traversable.In the case of non-radial motion along a hypersurface z=const we show that, asin the Kerr and Schwarzschild geometries, we should distinguish between orbitswith impact parameters greater resp. less than a certain critical value $D_c$,which corresponds to the unstable circular orbit of radius $u_c$ $(r_c)$. For$D^2>D_c^2$ there are two kinds of orbits: orbits of the first kind arrive frominfinity and have pericenter distances greater than $u_c$, whereas orbits ofthe second kind have apocenter distances less than $u_c$ and terminate at thesingularity at $u=-\infty$ $(r=0)$. For $D=D_c$ orbits of the first and secondkinds merge and both orbits spiral an infinite number of times toward theunstable circular orbit $u=u_c$. For $D^2<D_c^2$ we have only orbits of onekind: starting at infinity, they cross the wormhole throat and terminate at thesingularity.

On the cylindrically symmetric wormholes WhCR^e: The motion of test particles