Wall sign can't be edited, no matter the sign is in front of chest or not.
I tried right click and shift + right click the wall sign, nothing happened.
Maybe add a toggle like dyeing the sign is better.

• MC : 1.20.1
• Fabric : 0.14.22
• clickthrough-1.20-fabric0.83.0-0.4.1

Use /ctl off to completely disable the mod, then edit the sign, then /ctl on to reenable it. (Or press F9 unless you've rebound that key).