Deciding E1/E2/SN1/SN2 for cyanide ion
A general method for estimating $\mathrm{p}K_\mathrm{b}$ values is to use the equation $\mathrm{p}K_\mathrm{b} + \mathrm{p}K_\mathrm{a} = 14$ where $\mathrm{p}K_\mathrm{b}$ is that of the conjugate acid; in this case, applying it gives us $\mathrm{p}K_\mathrm{b}(\ce{CN-}) \approx 4.79$. We can generally assume that ‘strong’ and ‘weak’ in $\mathrm{p}K_\mathrm{b}$ terms are similarly to be defined as for $\mathrm{p}K_\mathrm{a}$ values. Therefore, cyanide is a weak base and the premise of this question is incorrect. This observation is consistent with the fact that neutral cyanide solutions are relatively safe as long as no acid is introduced to protonate $\ce{CN-}$.

Note that the general statement ‘the conjugate base of a weak acid is a strong base’ is incorrect. The opposite is often true, namely:


  The conjugate base of a strong acid is generally a weak base.


And vice-versa if you swap all occurences of acid and base. The word generally is required here, since compounds such as $\ce{H2Cl+}$ are very strong acids whose conjugate bases are still very strong — but these compounds are not typically easily accessable and certainly not in aquaeous solution. A weak acid needs to have $\mathrm{p}K_\mathrm{a} &gt; 15$ for the conjugate base to be a strong one but those are seldomly still considered ‘acidic’. An example would be water ($\mathrm{p}K_\mathrm{a} = 15.7$ therefore $\mathrm{p}K_\mathrm{b}(\ce{OH-}) \approx -1.7$) which is a weak acid with a strong conjugate base.

Since it is such a weak base, it has no access to $\mathrm{E2}$ pathways and $\mathrm{E1}$ pathways are disfavoured against $\mathrm{S_N1}$ if either is applicable. We don’t even need to consider $\mathrm{E1_{cb}}$. Thus, cyanide will generally react via an $\mathrm{S_N2}$ pathway unless the conditions for $\mathrm{S_N1}$ are much better.