A torque wrench is nice, but it can be done without it. Just ensure you have the correct size screwdriver or even a bit that goes in a socket. Just get that angle screw really tight.
Check the front-angled action screw. It needs to be very tight on the 77 to make it accurate. Also, check the scope mounts to make sure they are tight. Sometimes, poor accuracy in a 77 is due to the magazine box being too tight and binding the action. You can fix this by slightly shaving the box...
I had something similar happen to a rabbit beagle years ago. It was her left hip, and she would squat just like your photo. I carried her back to the truck and put her in the box. She was fine when I got the rest of the dogs up and then drove home. And it never happened again. She hunted again...
Do it, and don't overthink it. This is an opportunity to, in reality, make more money because you are working fewer hours. It's also an opportunity to work a consistent shift. On top of that, you will expand your resume by adding a management role to it. This may not seem important now, but it...