Yo don't need to change NLS_LANG env variables (btw, it is TERRITORY part that influences the first day of week, not the LANGUAGE part) on all your clients PCs if you can't or don't want to, it is sufficent to change the NLS_TERRITORY for the session where you want to change the ordering of the days in a week.

The following example will do this just fine:

ALTER SESSION SET NLS_TERRITORY = 'UNITED KINGDOM';

You can include something like that inside your application immediately after users log on, or you can create a database logon trigger and change NLS_TERRITORY in it for the sessions in which you want this to happen automaticaly.