Has abyone successfully converted a rear fixed sprocket or freewheel to a skip-tooth sprocket please ?
I always assumed that the modern" sprocket had the teeth at 1/2" centres and similarly, the skip-tooth teeth were at 1" centres.
For example a 19 tooth sprocket would convert to a 10 tooth skip-tooth sprocket - or is this just wishful thinking ?

There is no sense in doing this. The gear ratio you get is not actually about the number of teeth, it's the ratio of diameters of the chainring and cog. So a 44 in front and 22 in back with a 1/2" chain is equivalent to a 22 in front and an 11 in back with a 1" chain. No advantage to the 1" pitch. And you cannot get an cog that is equivalent in size to a 19 because 19 is not evenly divisible by 2.

I don't even understand the question beyond what noglider has added. "Converting" from a 1'2" to a 1" pitch chain is literally using a different cog and chainring, but both will have even numbers of teeth, as 1" divided by 2 equals 1/2", so there are no 1" pitch equivalents for odd-numbered 1/2" cogs or chainrings. You can find 1" pitch cogs and rings with an odd number of teeth but you need to multiply that number by 2 in order to find the equivalent 1/2" pitch cog or ring. On top of that 1" pitch chain is usually 3/16" wide, and almost every cog and chainring you will find are the same, so you can't just put a 1/8" wide chain on a skip-tooth cog/chainring drivetrain. Now go check the interwebs for the prices on 1" pitch chain, both roller and block type. Unless you are going for a piece-by-piece full restoration of a bicycle (probably pre-WWII, or a postwar track/path bike) using 1" pitch chain, roller or block, is so expensive as to be only a "sunday driver" for tweed rides or a wall hanger. I once installed a priceless NOS nickel-plated chain on an old pre-WWII path racer, with the shop owner watching carefully as I pushed that pin in and secured it with a nut. Insane amount of money spent on that restoration.
Phil

It would be a 20 to a 10. 10 minutes with an angle grinder.

Why do this?

OP didn't say they was looking for a different gear ratio. You're right about the results of course - counting teeth is just an easy substitute for measuring the diameter. It's such an odd question thought it makes me think they might have other reasons. And if not - it's just ignorance.

Hello,
I have a reason for asking this question - and it's not ignorance !
I have a pre WW1 bicycle with a skip-tooth chainwheel, which is in good condition, but the rear freewheel's teeth are badly worn.
I have a freewheel of the same era but it has ordinary 1/2" pitch teeth - and it's in good condition. It possibly has Italian threads.
I can't find a replacemment freewheel on ebay, with skip-teeth, so I'm considering alternatives.
These include machining off the worn teeth and using a readily available skip-tooth sprocket to make a new "tooth ring", which could be brazed on to the old freewheel.
Just a talking point really - as I'm still hoping to find a suitable skip-tooth freewheel from the distant past, which would have been nickel-plated !

Is there any reason a non-skip freewheel wouldn't work?

I had understood that 1" pitch chainrings, sprockets and chains were also wider than, say, 1/8" ones of 1/23" pitch. Or is this an instance where you can get away with running a wider chain on a narrower sprocket?

It surely looks that way, looking at the one 1" pitch crankset I have -- however, I have nothing in 1/2"x1/8" here to compare it with

PM me. I work for a shop that specializes in vintage bikes, with many esoteric parts from this era.
As for freewheel compatibility, I'll bet you a big shiny US nickel that your skiptooth freewheel threads aren't compatible with your proposed Italian donor. Depending upon the country and manufacturer of origin of your rear hub, you can have all sorts of threads or methods of attaching that freewheel to the hub. If you're restoring a bicycle from the early 1900s, don't cut corners (and teeth), do it right and get the correct part. If you're not already a member, join The CABE and post your query there. Again, you're welcome to PM me, after which I could put you in touch with my boss.
Phil

here is a threaded on skiptooth cog to fit a BSA freewheel threaded rear hub. https://www.ebay.com/itm/385293993992?var=653182991494 . they may be others available from another source. be aware that 1 inch pitch chains may require a different rivet tool, although i found that a park CT-3 works on a diamond skiptooth chain, but not maybe other brands or block chains. park CT-2 will do the trick though. old skiptooth cogs that mount on new departure, JC higgins or Musselman or other pre war hubs don't fit on modern rear hubs. it's a rabbit hole. and if you decide to build up a rear wheel with one of those old hubs with a sprocket already mounted, good luck trying to remove the cog to build the wheel. i ended up finding a hub driver as a part without a cog mounted, and temp replaced the existing one, then after the wheel was built, re-installed the original hub driver with it's hard to remove cog. the only reason i went to the trouble was for 1930's wastyn and 1940's sieber track bikes.