If you want that low of a divergence consider having a custom host built for you from one of the members here which uses a longer focal length larger diameter collimation lens and you won't need to use a beam expander and won't need correction with a cylinder pair to achieve that low of a divergence, or lower, for both axis of the diode output.
However, it will still be in the shape of a rectangle, regardless, unless the beam is somehow corrected to turn it into more of a square shape. For .5 mRad divergence of the fast axis, you will need a lens diameter of roughly about 25 mm. That will produce a "fat" beam, but it won't diverge nearly as much. You could also look at some of the 520 nm lasers sold by JetLasers.org or SanwuLasers.com and buy their beam expander, there will be more loss and lower power than a custom host using just one lens, but quick to get.
The Sanwu beam expander is about 3.3 expansion and won't reach .5 mRad with a one watt 520 laser diode unit, but the JetLasers will with their 10X expander, lower than .5 mRad. If the divergence going into a 10X expander is about 2.6 mRad, which is common using a collimation lens of about 6 mm diameter with a laser diode like the 1 watt rated NDG7475, the 10X expander in front of it should give 1/10 that amount of divergence.
