Yes, that's the same size as my right hand.
Buckle down on fingers 1343, and if you're feeling the strain, you're using the wrong technique.
This fingering is by far THE fastest. If you can apply the correct technique at a slow tempo with a good interpretation of the melody, then that's when you start increasing the speed.
With the trill passage, have a go at fingers 35353535, over 454545454545, with the octaves. finger 35 is my preference, but if you like 45, then that's fine too.
Even Yundi Li uses this fingering.