I clip somewhere between 1/3 and 1/2 of one wing.
It doesn't seem to do them any harm.
I have several queens which I clipped a couple of years ago still going strong.
I think a queen is more likely to get balled after she is marked as the bees can on occasion take umbrage at the smell of the marker.
If in doubt, mark and clip in spring after the queen has overwintered as she is less likely to be rejected, so they say anyway.
Not many complain that marking is cruel.