Just to answer your question more clearly...
You would need to file an ATF Form 1, first. You will need your local Chief Law Enforcement Officer (CLEO) to sign off on the form, or you can form a trust or LLC, then no sign off is needed.
You will send the form, fingerprint cards, photo, and a check for $200 to ATF. Then wait. And wait. About 6 months, some come back sooner, some longer. In the meantime, you'll need to get it engraved. If you got CLEO to sign off, you'll engrave your name, city, and state, per guidelines in the NFA handbook. Look it up, as it must meet certain requirements. If you went the trust or LLC route, you will engrave your trust or LLC name, city and state.
When you receive your form back from ATF, with your tax stamp, then and only then can you shorten the barrel, or have a gunsmith shorten the barrel.