To answer OPs original question,
YES, you can replace a barrel on the factory 10/22 with a shorter one and remain NR as long as it meets 26" (660mm) OAL.
This is to be done in firing condition (muzzle devices included when installed and torqued on)
Muzzle devices do count to OAL length, but not barrel length.
The shorter barrel needs to be manufactured to that length, i.e. You will have marking on the barrel indicating length and manufacturer, which stand for proof that it was not cut down under 18" (altered)
I have seen factory 10/22s with 7-8" barrels in a chassis that meet the NR requirement.
Changing the barrel is a part replacement, it is not an alteration as the original factory production state was not altered. It is not a permanent change, meaning the factory barrel can be reinstalled at any time, no different than swapping a trigger or stock. Cutting a factory barrel is an alteration as you cannot return it to the original condition.
This has been argued many times online here, it is legal to change barrels with aftermarket barrels of shorter length. Ones personal opinion does not change precedence.