Even if it isn't a problem at the "firearm" level because it's an antique (and, while I personally wouldn't try because it'll do more harm than leaving it alone, I suspect the fact that it's an antique overrides the serial number laws) you need to be aware that many states have laws against removing serial numbers on all sorts of devices.
E.g.
Montana 45-6-326. Obscuring the identity of a machine.
(1) A person commits the offense of obscuring the identity of a machine if he:
(a) removes, defaces, covers, alters, destroys, or otherwise
obscures the manufacturer's serial number or any other distinguishing
identification number or mark upon any machine, vehicle, electrical
device, or firearm with the purpose to conceal, misrepresent, or
transfer any such machine, vehicle, electrical device, or firearm; or
(b) possesses with the purpose to conceal, misrepresent, or
transfer any machine, vehicle, device, or firearm knowing that the
serial number or other identification number or mark has been removed
or otherwise obscured.
(2) A person convicted of obscuring the identity of a machine
shall be fined not to exceed $500 or be imprisoned in the county jail
for a term not to exceed 6 months, or both.
(3) The fact of possession or transfer of any such machine,
vehicle, electrical device, or firearm creates a presumption that the
person knew the serial number or other identification number or mark
had been removed or otherwise obscured.
Might be setting up a trap for you or someone else down the road.