The actual hinge is very simple and in the dismantled state very easy to replace, see the first photo.
The problem is that, when assembled the middle shell gets in the way but the edge/lip of the top shell is VERY thin and you may be able to prise it up enough to get the hinge back inside the drone's body, see the second photo.
BE WARNED there is a cricuit board directly under the lip of the top shell, exercise great control over your prying tool and DO NOT allow it to penetrate deeply into the drones body, see the third photo.
The second photo is of an undamaged
Mini 2 and I used a scapel blade (not ideal) to prise the lip of the top shell up enough to allow entry of that shaved down match stick. I think the match stick would need to be thicker to allow the hinge to enter but I would shave several match sticks to differing thicknesses and gradually widen the gap.
Heating the upper shell to "warm to the touch" with the likes of a hair drier might make things easier.
I would wait and see if anyone offers alternative methods before trying this and also try a search of the forum for Mini battery cover to see if you can find other threads dealing with this