(0.4-0.25)/2=0.075mm anular ring which is smaller than even the 0.15mm anular ring requirement on the thinnest copper option.
You need at least 0.25+2*0.15=0.55.
And also remember that drills have tolerances. If the drill has +/-0.05mm tolerance i would not go below 0.6mm via diameter for a final nominal hole diameter of 0.25mm.
In your case this is all you need to think about. Acourding to your datasheet the anular ring is given as AR = (pad size - final hole size)/2
Some fabs give the anular ring requrements differently and you might even need to think about the difference between final hole diameter and drill diameter.
The drill is a bit larger than the final hole. (my fab told me they drill with +0.1mm.)
If this would be the case this would mean you need 0.7mm minimum via diameter.
But again this really depends on your fab.