There is no other place to get the tractor SN other than the data plate. There are ways to estimate the age, by engine SN, casting codes etc.
As for the air cleaner, you may or may not have the original to the tractor.
First, we must determine what tractor you really have. Do you have a TE-20 or a TEA-20? Use the provided picture to help determine the type of engine. i.e. where is the oil fill. If at front you have a Continental engine (TE-20) if at rear you have a Standard motor (TEA-20).
The later TEA’s had a dash screen air inlet which this hose you describe hooked up to. I am thinking that you may have an original air filter but a replacement dash, which could explain the missing tag. If you later model year tractor receive the dash from an earlier year tractor or even a different model (i.e. TO-20) then the tag would have been removed to eliminate confusion.
Even if it is a replacement air filter, it should not matter much as the only difference was where the air was taken. However you may want to fashion a screen over the opening.
Another possibility is that you have part of a pre-cleaner assembly.