As our family gunsmith (may he rest in peace) used to say, with his trademarked Snidely Whiplash evil grin, "Any project is feasible if properly funded."
So yes, it can almost certainly be done, and a pretty wide variety of shops can handle the work well. Even if the barrel is a bit too thin for certain current choke tube systems, there may be a thin-wall choke tube system that will work in it.
Far as I know your gun is a fixed barrel design, which may complicate things a bit. That means you'll have to leave the whole gun to get it worked on and can't just drop off or even mail in the detached barrel, as I've done with several barrels in which I wanted to get choke tubes installed. And it may also mean the shop will have to unscrew the barrel from the receiver to do the work, and then reinstall it after it's shortened and threaded. That complicates things, which might make it cost more, and opens doors for possible bigger problems like a torqued receiver if the shop doesn't do everything right.
I sincerely hope you get what you want out of the process, and the gun runs forever... if you have a gun that fits and you're wise enough to know it, you're already luckier than the average shotgunner.
lpl