Here, this is a 1° allylic halide. If it goes by SN1, the intermediate will be resonance stabilised.
Also, since it is 1° Halide, it can also go via SN2. Which one will be preferred?
This reaction will happen by both SN1 and SN2 mechanism, apart from this SN1' and Sn2' (allylic mechanism ) will also occur. Thus from SN1 and Sn2 one will get primary cyanide and from SN1' and SN2' one will get secondary cyanide .( read organic chemistry by jerry march for the detailed explanation). I am attaching a screenshot of clayden which explains this beautifully.
Although I haven't found this exact example in the literature, I suspect this reaction is exclusively SN2.
The analysis with respect to the electrophile is good: the allylic leaving group is suitable for both SN1 and SN2. That means that the other conditions will determine which is preferred.
Cyanide is among the best nucleophiles for SN2 reaction. First, it is negatively charged. Second, because it only has two atoms, it is extremely unhindered.
As @CupC_56 suggests, solvent (unlisted) could play a role. However, typically for SN1 reactions, a polar protic solvent acts also as the nucleophile. If one was trying to obtain a nitrile product, it would be a poor choice to run the reaction in the presence of a polar protic solvent that would (1) reduce the nucleophilicity of cyanide and (2) compete with cyanide to react with the electrophile.
Well, Your Question seems a bit off as the type of solvent has not been mentioned. Is it:-
Obviously, SN1 can occur only in Polar protic solvents, and in reactions where the alkyl halide is a conflicting one (reaction can occur both by SN1 and SN2), the mentioning of the said solvent is essential.