When you swap teams in the Spawtz Application you do so via the Teams/Divisions button next to the league you are interested in.

Check the checkbox next to the two teams that you want to swap.  Then go down to the bottom of the page where there is a "Swap selected teams" function. 

Within that function there is a "Keep results before" field.  If you check the checkbox for this field and then select today's date in that datebox, all results and fixtures PRIOR to today will not be affected, but all results and fixtures LATER than today WILL be affected. 

If you want for THIS week's fixtures to remain unaffected as well then you should set the "Keep results before" date to some date later than this week - say the Saturday or the Sunday of the week.