ASI does good work and would be willing to do a smaller job, but you will pay dearly for it.
Any local gunsmith should be able to do a simple procedure like that.
A gunsmith will remove the barrel and do the work on his lathe. The preferred method for sure but that will up the cost considerably.
There is a low cost alternative, if you are at all handy, do the work yourself.
I have shortened several Minis doing the work myself, and it is not difficult at all.
The barrel does not need to be removed for this method.
You would need $50-$70 worth of hand tools, once purchased you would have them to do future Minis or sell them and get most of your money back.
I'd allow an extra 1/4" just so you don't run afoul of the law and end up with an SBR.
Mark barrel and cut with metal blade in a chop saw. That will be a straighter cut than using a hacksaw. I've used a hacksaw and it works fine, but I have a facing cutter for my hand-tool handle to square up the cut if it is off.
This is an older Mini-30 with single blade front sight, barrel is cut right behind the sight with hacksaw using the back of the sight for a guide for saw, barrel ends up at 16 .25"
I also crown with cutters in various angles, 11, 30 and 45 degree that thread onto the handle, and those cutter head have a threaded hole on the front that can take different caliber bore guides.
You could get by crowning with a hand drill and appropriate bit. Crowns done on Minis at the factory aren't that great, it's not too hard to improve on them.
I use dies (1/2" - 28 for 5.56mm, and 5/8"-24 for 7.62 x 39mm) to thread the barrel for a flash hider or brake, that tool (die, handle and bore guide) will run you another $65 or so). I have done several Minis with the threading tools and they have paid for themselves many times over, saving me $100s in gunsmith fees.
Here the barrel is starting to be threaded with die, handle and .30 caliber guide below it:
The front sight is placed along side the barrel where it will go, and a mark made on the underside of the barrel with a black marker.
That is where the notch for the roll pin that holds on the sight will be cut.
Ideally you will have a vertical mill, but the notch can be cut with a drill press.
There is a simpler and easier method, cut the notch with a file.
You can use a triangle file, and finish up with a small round file like one used to sharpen a chainsaw blade.
Make the notch 1/2 the thickness of the roll pin. I'd go a bit less as the roll pin has some give to it, and you don't want to end up with it loose.
You have to ensure the notch is at the very bottom of the barrel or your sight could end up canted and you'll use up too much windage on the rear sight trying to get zeroed.
The front sights are real tight on the barrel, Ruger won't sell you a new sight as they say the carbine has to be sent to the factory to be installed with a hydraulic press.
But I use a piece of Oak or other hardwood and hammer the sight in place with the wood against the sight.
Here is the front sight re-installed on the shortened barrel with a flash hider on the threads. I would have tried to upgrade the old single blade sight with a newer style winged take off sight, or ordered one of the M1A style sights from Cogburn Arsenal, but this Mini was for my daughter.
She has good 23 year old eyes and will be using the Burris Red dot 99% of the time.
If you made the cut on a chop saw, and found a bit to crown (bevel) the muzzle, you wouldn't even need the Brownells hand tools I mentioned.
The Mini shown was stainless, a blued one would just need some touch up with cold blue on the muzzle.
My daughter's 16 1/4" Mini:
And my synthetic stock Mini that I shortened to 16 1/4":
