The weapon fires normally.
These benefits only apply when the item’s wireless mode is on. (Wireless Bonuses, CRB 421)
The trigger is a manual trigger, it's a mechanical system. It isn't affected by the smartgun system and will work even on a dead zone (no wireless connection).
A smartgun with the touch system (no trigger), wouldnt work though if you remove the fire command.
What you could do to mess with an enemy is replace the lock target with the eject command, that way, when they aim at someone with his smartgun and try to obtain that +1 bonus, his weapon will eject the clip.
Remember that some smartguns can even fire mentally, without someone even holding the gun.
In 4ed Arsenal we had Eletronic Firing (could be applied to any gun) and Trigger Removal (smartguns only), which explain how to replace the mecanical trigger with one controlled eletronically:
Electronic Firing: With this modification, most of the weapon’s moving
parts are removed and it fires electronically, meaning that an
electrical signal detonates the bullet’s propellant. This provides 1
point of recoil compensation (for restrictions on recoil compensation,
see p. 148) and a –1 dice pool modifier to sound-based Perception
Tests when trying to locate where the weapon is being fired from.
Electronic firing is usually combined with trigger removal (see p.
153) to further reduce the number of moving parts, but this is not
mandatory. The weapon still includes a loading mechanism that moves
the bullet into the chamber, and it requires caseless ammunition.
Trigger Removal (Smartguns Only): The time needed to mechanically
pull a trigger might just be the fraction of a second, and the deviation of the barrel due to the movement of the trigger finger just the fraction of a millimeter, but this is enough for many professionals to instead rely on wireless commands. The game effect of removing the trigger is negligible, but the gun can no longer be fired manually. A weapon without a mechanical trigger can only be fired by wireless command, via skinlink or smartlink, or over a fiberoptic cable that connects the weapon with its user’s datajack.
In 5ed core book, the Smartgun System says you can fire the weapon without pulling the trigger, but it does not say you replace the mecanisms:
Smartgun system: This connects a firearm or a projectile weapon
directly to the user’s smartlink. Incorporating a small camera and
laser range finder, the smartlink keeps track of ammunition, heat
buildup, and material stress. If you have a smartlink, you can
mentally switch between gun modes, eject a clip, and fire the gun
without pulling the trigger.