In general, you want the sear spring and sear engagement to be no stiffer than is needed for safety.
But as for whether or not it will work as it is with your triggers, that's not hard to test. Put a flint-sized piece of wood in the jaws of the cock (not a flint, lest it cut you), and while wearing a pair of leather work gloves (so you don't get pinched), you can set the lock and set the trigger and then just hold the trigger bars up to the sear and then trip the trigger. The rear trigger bar should pop up and release the sear, even if you are just holding the lock in your hands. (Just try to keep your fingers out of the way of the cock and the frizzen movement.)