A 7 speed freewheel is generally for 126mm hubs. It's unusual for your hubs to have 130mm and would imply that they have been modified. Anyhow with them being spaced at 130mm the 7 speed should work with no problem what so ever.
You say the 7 is wider than the 6 by a few mm, looking at the frame do you think that you have the clearance required?
Well, I've screwed the freewheel onto another hub to test with the frame and clearance appears OK for a chain but I can't confirm that the test hub spacing is the same as the Record hub. I guess it's a case of trial and error but was keen to find some known facts. I really want the final build to feature the Campagnolo freewheel without too much pain eg redishing etc.
Thanks for the answer by the way.