the right way to set up a freewheel is using a spacer as needed to set the backspace for chain clearance. they come in 1, 2, and 3mm thicknesses and you can stack them for the desired thickness.
the other issue you'll run into is if you use a 7 speed shifter with a 6 speed freewheel, you'll likely have issues since there is extra travel in the derailer for the extra gear. You can adjust the travel of the derailer, lock out 1 gear on the shifter, or replace the shifter with a 6 speed.
It may also be possable to mount a 7 speed freewheel, however you will need to stretch the frame slightly to accomidate. Using 1 of those washers on the outside of the dropout, but placed inside the dropout will likely give you the spacing you need.