I built up a old Rudge frame with a fixed wheel years ago.
with a front brake.
it had rusty rims and a bent crank.
so it sawed through a set of brake pads in a day....and my legs

I dont have a fixed hub. That one I had was likely to be a 40 spoke.
not got many rims with that many holes. Maybe a couple of stainless rims...too heavy.

I might go to the bike shop and search there wheel pile. Its a pyramid about 40 feet across and 15 feet high.
Im wanting a Raleigh Chopper I was told they had. Also might get a Peugeot racer for its 700c wheels and aero levers. They had a Raleigh All Steel to. But it was more All Rust. And looked about 23". Too big