Oh, actually I'm glad to hear that.
In that case, relacing is definitely the way to go. Remember to remove your freewheel FIRST...
H+ Son TB14 is well regarded, and looks a little like an old Mavic clincher or something.
I've used the Sun M13II, which looks exactly like an old Rigida if you peel off the stickers, except they are much stronger.
Both come in polished aluminum and are widely available. Google or ask your LBS.
Oh, there is also Velo Orange, and Pacenti, and probably some other purveyors of vintage look rims.
If you want to cheap out, get a set of prebuilt Sun M13II + 'generic' hubs from velomine or wheelmaster. Throw out the quick releases, but the cost is less than the spokes and rims alone, and the hubs are not bad.
https://www.amazon.com/WheelMaster-7...-search&sr=8-1