How do you take the shine off a Remington stock or BAr without a complete refinish job ?

Try fine abrasive paper [600 grit], wet/dry ,with water.The other option would be steel wool ,0000.I found the paper better.

0000 wool will dull it to a somewhat satin look.....you may wish to dull it more however. It's not a bad first step

Ive found that mud and/or being banged behind the seat of a truck usually does the job.

There actually is 'dulling spray" available which is a flat clear laquer or poly. That way you would not have to remove any of the factory finish and could renew the dullness later with more spray.

A little rotten stone mixed with linseed oil to form a paste will dull your finish without removing much of it. Rub it lightly, it doesn`t take much rubbing to knock the shine off.

0000 won't do much but polish that hard finish...A wet sanding with 360 grit wet or dry will cut it back and you can refinish it pretty fast that way....

Rottenstone and oil paste mix rubbed with a red or grey scotch pad will also cut it back to a dull finish...

The finish on the Rem and Brownings must be a dipped finish as it is thick and hard...