Some misinformation, there. Prior to 1968, any gun could be ordered through the mail. There was no "form", the only requirement was that a handgun buyer had to enclose a signed statement (could be handwritten) that the buyer was "21 or over, not an alien, not convicted of a crime of violence, not under indictment, not a fugitive from justice or a drug addict." (Quote from Klein's ad, Dec. 1960 American Rifleman)
The same statement, required by Federal law, was also required for purchase of a handgun from a dealer. There was no prohibition on interstate sales of any firearm, even an auto weapon, if NFA rules were complied with.
However, many states had more rigid control, including waiting periods, police approval or police permits.
After 1968, mail order sales were banned, and interstate sales were prohibited except for the contiguous state rule mentioned above. To make that exemption effective, both states had to pass laws allowing it; some states never did.
The 4473 was green, but any requirement to send a copy to the police was local, not part of federal law. There was no "waiting period" or police approval under federal law, but many states had or would have such a law.
Unless the buyer was known to the dealer, the dealer was supposed to have a valid ID for the buyer, and check it against the 4473, but many just accepted whatever the buyer wrote down without checking. Except as required by state law, dealer sale of a handgun was no different than sale of a long gun.
Jim