In the shadowbox-mootools.js adapter, find the animate() function and change
var anim = new Fx.Styles(el, config);
var anim = new Fx.Morph(el, config);
That should get you up and running.
However, be aware that
a) the version 1.2 code I downloaded from the mootools download area was still versioned as '1.2dev' even though it is being promoted as a firm release
b) there seem to be a few problems with fading (ie opacity). The shadowbox adapter attempts to overidde setOpacity() but this has no effect on v1.2 (not sure about v1.1!). Even if it did, mootools' retrieval of current opacity from its internal storage is returning 0 when I can plainly see that it is 1, so fading out the 'loading', for example, just isn't working. This might be due to shadowbox's handling of visibility/opacity but if it is I can't find it. It would seem to indicate, though, that mootools might not play well when combined with native setting of an element's style values
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