Yes it's perfectly doable with a few considerations. The first being, is it bound? If so, I'd agree with trying to find another neck. If it's not bound, I've thinned a neck this way by filing the sides down evenly with a large file and working slowly. I use a smaller half-round file to blend the areas around the nut into the sides of the headstock. Closer to the end, I switch to a sanding block with around 120 grit and then up to 220 then fine hand sanding. After that, I redo the fret ends and dress the frets.
You'll probably have to refinish the back and sides of the neck, but you can easily do this without disturbing the headstock face or flat of the back. Another consideration is how deep the side dots have been installed - I've not run into a problem with this, but it's theoretically possible if very thin dots were installed. Worst case scenario, you have to replace a dot.
It likely goes without saying but you'll also need to cut a new nut, unless you like your strings really close to the edges of the board.
This works easiest going from 1.625" to 1.5" (or 1/16" per side), but you can also narrow a wider neck, though you'll end up shaping the transition to the headstock edges more.
Post up here and the hive mind can help problem solve and point out potential pitfalls.