Can you add the operative trait to the syringe that is used to do the melee injections?
Since the class is supposed to use DEX as a secondary ability score doing it as a normal melee weapon based on STR feels very odd.
Most Biohackers will not invest in that ability score and therefore will be far worse in using their injections in melee range than otherwise.
I'd like to second that motion-using a syringe is often far more about finesse than impact
I'll also say this would likely be a better synergy for the class to have injections use the operative tag.