Thank's for the hint to the rooting thread. Here is the related post:
So, all you need to do is navigate to /system/usr/keylayout/ via root explorer, remount as r/w and append the following lines to gpio-keys.kl:
key 105 SPACE SHIFT
key 106 SPACE
Unfortunately, SPACE+SHIFT does not work on most apps. The best compromise for me is having only page right mapped to space and page left kept at stock settings. This will allow fast forward in android menus, filemanager, etc and also work as page forward in stock browser.
For myself, I don't care about Sony Apps as they can be controlled via touch screen. And I frequently use apps like Dolphin Browser, iRealb and Bible Reader which greately benefit from page turns.