Whatever you do needs to be done accurately, or the reamer will not cut to size or parallel (depending on how firmly it is held). In my limited experience of such work, I would look at the expense of grinding the shaft. Not centreless grinding, but relying on the centres in both ends of the reamer (which is how the reamer was held to grind the blades.). And I would then look at the cost of a new larger holder instead, or modifying the existing one, and using the bigger hole rather than reducing the reamer itself.
I expect a decent carbide tool might 'do the cutting' but I doubt whether the finished result would be accurate enough, in terms of concentricity etc. So, I suggest that you would need to do the work between lathe centres, and be 100% sure that your centres were properly in line with the bed. And this depends on whether you intend to hold the reamer for the intended job relying on the newly thinned shaft. If not, then ignore my comments about dead-accurate holding, but remember that you may have buggeredup* the reamer for some later jobs.
I await with interest the feedback from those to whom this sort of exercise is a weekly task.
* this everyday engineering word is not in my spellchecker. I can't think why not …
Cheers, Tim