Never mind that many wedge-fit axe heads actually have a waisted eye that's narrowest about 2/3 of the way down the eye rather than a constant taper top to bottom.
I have only ever seen this on drilling hammers myself, but I don't doubt that there are axes made this way.
As far as in the field vs a shop, when I started in the hobby of axes as a teenager all I had to work handles with was a hacksaw a 4 in hand a hammer and a knife.
I might as well have been doing this in the wilderness.
If I had to do this in the field unexpectedly I'd just have to be careful or cut a little further down and whittle on the excess.
If planning for this I'd just take my MXZ folding saw with me since it takes recip blades.
I don't have one of the leatherman models that uses replaceable T shank blades but those models are popular and with that the worry of dulling your saw is alleviated.
To knock it out just use the broken handle or any stick and hit it with anything you can find.
To hold the head steady just bury the bit into whatever stump you were using around camp...etc
I have put an axe basically in my lap while clearing out the eye, not easy on my legs but I've done it a time or two
when all my good tools that I inherited from my grandfather were at my dads house and I lived with my mom, I had almost no tools and made do with whatever I could as a teenager.
On paper it's easy to say that a wedge fit rehang would require this and that or it's much harder because of this or that, but I've removed bad handles with almost nothing before with minimal effort.
Just a saw a striking implement and a drifting implement.