For an electron arrangement diagram, is it necessary to show the inner electron shells or is it customary to only show the valency electrons?
Both are correct: for $\ce{Cl-}$, the inner set of electrons would be implicit, as $\ce{Cl}$ has 17 electrons. The point of drawing these orbital diagrams, especially in a molecular context, is to show the nature of bonds and to show how the octet/duplet rules are being followed. 

If you have difficulties in using the second diagram (finding it harder to read or are confused by the similarities in $\ce{H}$ and $\ce{Cl}$), you should use the first diagram.