Check it out ... the airboat captain faces off against a massive alligator during one tour down in Louisiana. Jeremy proves to be a pro at handling the large reptile ... though, he jokes he's less skilled in his personal life -- taking a jab at his ex-wife in the process.

He tells the tourists aboard his boat ... "Me and [the alligator] have been pretty tight ever since I fed him my ex-wife. I'm just kidding. I'm kidding."

Though Jeremy is clearly making a quip, it certainly raises eyebrows given little is actually known about the everyday joe who's captured the singer's heart.

TMZ broke the story ... Lana and Jeremy appeared ready to take the next step in their relationship at the end of September after the pair obtained a marriage license from the Lafourche Parish Clerk of Court.

Not long after this news broke, Lana and Jeremy were photographed exchanging vows in a ceremony held at Airboat Tours By Arthur in Des Allemands, LA ... where Jeremy is employed.

Lana has since spoken out in defense of her new husband ... who she was first romantically linked with back in August. The singer praised Jeremy as her "one and only" and "amazing" after paparazzi footage captured the pair enjoying quality time down south.

Per Lana, a local couple has allegedly been flying drones outside her and Jeremy's property ... disturbing their newlywed bliss.