Just handling it isn't a problem. Trying to BUY one and entering false data on the ATF form would be. Accepting a gun from someone who did a straw purchase would also be a problem.
I heard Harry Litman explain the super technical legal details about this.
Technically, the law says that Trump is not allowed to receive a firearm which has ever crossed state lines (i.e., was not manufactured in and never left the state). I assume that "state line" thing is necessary for this to be a federal law.
While your two examples (buy/lie or accept from a straw purchaser) would also be illegal, the act he is photographed in may be technically illegal. "Receive" raises the real question. The law doesn't say "purchase." It doesn't say "take ownership of." It says "receive."
"To acquire or get something. Someone can receive an item such as a letter or a gift or can receive something non-tangible such as a word of encouragement or praise."
He didn't acquire or get the gun, he held it for a photo op.
There is no amount of shenanigans that will land him in jail before trial, and maybe even after. Dude was charged with trying to overthrow the government, and he got released on bail.