I wouldn't.
First reason: I'd be concerned about reliability - as per
@Tim0712 you'd have to open up the gas port, and then figure out timing and reliability. Second reason: they're not making any more of these and if you booger it up you'd have to re-barrel it, which would mean rolling the dice on a (probably used) replacement barrel from Numrich or eBay, assuming you can find one.
As far as that goes, it would probably be smarter to have your 'smith re-barrel your gun with an actual carbine barrel, and hold on to the original barrel, instead of chopping it. You could probably find a carbine barrel in .35 Whelan, as far as that goes. It might be cheaper to find another auto carbine.
For what you'd spend chopping this rifle you could get a used levergun in .30-30, .444, .45-70, .44Mag, .45LC, .35Rem, .32SPL, .38-55WIN, or whatever. Or a used bolt gun in 35 Whelan, .358Win, .338Fed, .308, etc.
Really, 4" of extra barrel isn't going to make all that much difference in handling in the field, and if you're hunting in cover so close you can't handle a rifle, you should probably sling it and switch to a handgun.