I doubt it'll get much lighter when converted to a single speed.

This frame very likely uses the now obsolete rear dropout spacing of 126mm. You won't be able to find an off the shelf new wheel to fit this spacing. You'll need to have a shop narrow a modern 130mm spaced wheel, or space out a 120mm track width wheel. This bike likely also uses the obsolete 27 inch rim size. Todays 700c rims are a little smaller. This change may require brake calipers with a longer reach.

You don't necessarily need to change the crank to go single speed. It is possible to take off one chainring. In fact, that is the most common way these days to procure a single speed crank for an old bike.