Impossible? Never heard of the word.
Looking at the picture above, it appears that the axle does stick out a bit beyond the wheel. It might be possible to make a tool to apply pressure to the end of the axle and perhaps on the hub of the wheel, lessening the chance of breaking the wheel. I would not apply pressure to the rim of the wheel; to do so would be taking a big risk of breaking the wheel.
I personally think it is possible to unsolder the wheel, straighten the axle, and solder the wheel back in place. I have unsoldered many things over the years. It would be a bit of a touchy process, though.