No, that wouldn't be legal. The outer shell has a serial number. If you want a suppressor....step one is to purchase one. The reason for this is to create ownership of the device and serial number. But, you can't take possession so the shop and you will fill out all of the paper work to be submitted including fingerprints, the serial number, $200 payment for the tax stamp, etc., etc. Some months later the gun shop will call and say your tax stamp has come in and you can drop by and pick up the suppressor. There are several options for ownership. You can easily dig into the details on the net if you want the entire story.
On the other hand there are devices sold that will thread onto the end of your barrel which allows you to screw on a new oil filter. The first shot punches a hole in alignment with the exiting round. They work well if you tube videos can be believed.
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If you wanted to protect a nice looking suppressor the best advice would be to just take care of it. Several of my pistols look brand new after occasional shooting during the past 10 to 15 years. P22s get drug around, carried through dust and dirt, shot a lot, laid on the truck floor, truck bed, ground....if the suppressor is attached...so be it. I suppose you could also wrap the cylinder to protect it. They do get hot, even on .22's, when fired rapidly.
I caught a Silencer Co SS Sparrow on sale for $229 a few years ago. Perhaps Ky Gun Co. I bought it, they shipped it to a class three dealer here. We completed the paperwork. They held the suppressor. So, suppressor $229 and tax stamp $200. Nine month wait. You could always put a protective sleeve over the entire part. They are very simple. Cleaning is one issue....the dirt they blow back into your pistol is another. 1917