... didn't realise how bad it was. Now he's shown and explained it I'm going to do a shook swarm on his advice. They are building up but only on about 4 frames so I'm thinking poly-nuc would be best and if they recover quickly - as I've read they can - transfer to a national but if not leave to over-winter in the poly.
I don't like second-guessing a Bee Inspector, but a shook swarm (rather than a special form of Bailey comb change) is unusual advice for a very weak colony.
The special form of Bailey is to use fumigated drawn comb in the 'new' box, and to dummy down (both boxes equally) as far as possible.
In that case, or in the case of a shook swarm onto fumigated drawn comb, the need is to ensure that the colony has some stores in reserve - and thus feeding some (a couple of pints?) strong syrup (like imperial 2:1 or Ambrosia) would be appropriate. And perfectionists would suggest a contact feeder for the weak colony - though that can lead to problems with for example metric 2:1 crystallising and blocking the feeder.
However, for drawing foundation, thin syrup (about 45% sugar, like imperial 1:1) is the appropriate feed to give.
However, a weak colony can't draw comb very quickly, so the beekeeper must be very careful to avoid feeding faster than they can consume. Some stored reserve is necessary (initially, the feeder suffices), but you have to avoid the bees filling their precious comb with syrup and nectar being evaporated down for storage.
Having clean drawn comb available for use in such situations is extremely valuable.