The American Synthetic Suppressor-Ready weighs 5.4 pounds, the Pro Varmint is 7.3 pounds. Their page, cz-usa.com.

 

You might shave a pound or so off the weight of the rifle by switching to a Synthetic American ( or inexpensive aftermarket) stock. Still, that weight will mostly come off the rear of the rifle and cause the gun to feel more muzzle heavy. IMHO, it's not going to give you the difference you are looking for ( and/or worth the cost and effort.)
A new Synthetic American with 20" SR pencil barrel will only cost a few hundred more (at $420 or so). That American will be allot lighter, better balanced, tough as nails and likely just as accurate. I'd just buy a second rifle dedicated for a walking rifle. If need be, you can always sell your current rifle ( or pieces there of ) to fund the project.

 

You might shave a pound or so off the weight of the rifle by switching to a Synthetic American ( or inexpensive aftermarket) stock. Still, that weight will mostly come off the rear of the rifle and cause the gun to feel more muzzle heavy. IMHO, it's not going to give you the difference you are looking for ( and/or worth the cost and effort.)
A new Synthetic American with 20" SR pencil barrel will only cost a few hundred more (at $420 or so). That American will be better balanced, tough as nails and likely just as accurate. I'd just buy a second rifle dedicated for a walking rifle. If need be, you can always sell your current rifle ( or pieces there of ) to fund the project.

This.

My 20" pencil barrel 457 does 0.3" to 0.4" 5 shot 50 yard groups in the hands of an untrained teenager and with cheap ammo. It weighs Sweet Fanny Adams.

 

In making this suggestion, I am assuming that you are carrying the rifle, slung over your shoulder. Doing that messed up my neck too but a backpack that had a pouch for the rifle made carrying much easier. It was a Badlands brand.

 

Also assuming that you sling carry over your shoulder. I made the move to Safari Sling for all my rifles several years ago. The Safari Sling keeps the weapon in front of me and ready to shoulder for a shot. It also distributes the weight across my shoulders and upper back.... here's their video....