I would have to see exactly how much room there is in the trigger area to install set triggers.
They do take more space, not only in the stock under the lock but in the bow of the trigger guard.
The first question is, Does your existing lock have a "fly" in it?
With the common double set double lever set triggers, the fly is needed to allow the hammer or cock to fall from a fully cocked position to the fired position without your finger holding the trigger back.
To find out if your lock has a fly, take your unloaded gun and point it in a safe direction.
Then, fully cock the gun so it is ready to fire.
Hold your thumb on the hammer or cock and gently pull the trigger just far enough to release the hammer. Keep the hammer/cock from falling with your thumb.
With the hammer/cock restrained, now take your finger off of the trigger.
Now, allow the hammer/cock to fall slowly. It may hesitate when it reaches the half cock notch location.
Now is the moment of truth.
If the hammer/cock continues to fall to the fired position, your lock has a fly in it. A double set trigger will work.
If the hammer/cock stops because the half cock notch has captured the sear, you cannot install a common double set trigger even if you find one that will fit.