  The exocometary origin of CO gas has been confirmed in several extrasolar
Kuiper belts, with CO ice abundances consistent with Solar System comets. We
here present a molecular survey of the $\beta$ Pictoris belt with the
Submillimeter Array (SMA), reporting upper limits for CN, HCN, HCO$^+$,
N$_2$H$^+$ and H$_2$CO, as well as for H$_2$S, CH$_3$OH, SiO and DCN from
archival ALMA data. Non-detections can be attributed to rapid molecular
photodissociation due to the A-star's strong UV flux. CN is the longest-lasting
and most easily detectable molecule after CO in this environment. We update our
NLTE excitation model to include UV fluorescence, finding it plays a key role
in CO and CN excitation, and use it to turn the SMA CN/CO flux ratio constraint
into an upper limit of $<2.5$% on the HCN/(CO+CO$_2$) ratio of outgassing
rates. This value is consistent with, but at the low end of, the broad range
observed in Solar System comets. If sublimation dominates outgassing, then this
low value may be caused by decreased outgassing for the less volatile molecule
HCN compared to CO. If instead UV photodesorption or collisional vaporization
of unbound grains dominates outgassing, then this low ratio of rates would
imply a low ice abundance ratio, which would in turn indicate a variation in
cometary cyanide abundances across planetary systems. To conclude, we make
predictions for future molecular surveys and show that CN and HCN should be
readily detectable with ALMA around $\beta$ Pictoris for Solar-System-like
exocometary compositions.
