The problem with copper is that it is between Bismuth and Steel on the low end of density. Plus it must be annealed to be soft enough not to score barrels. Then the price is a little high at $2.00 a pound. It might work as a lead shot replacement but I'd rather use Bismuth if you can get it.
Copper shot is softer than TMX and TM, steel and hevi shot, your only other options are niceshot or bismuth,
Nice shot is about £80 / KG here. - Each cartridge has £2.40 worth of shot in it assuming 30 gram loads.
Busmith is running at £61 / KG - each cartridge has £1.80 worth of shot.
ITX is harder than copper and thats £50/ KG - which mean a 30 gram cartridge is £ 1.51 worth of shot.
Copper is £18.40 / KG - making each cartridge cost 0.55 pence next to steel copper is the most cost effective - Im going to experiment with a card shot cup - im not convinced there will be any scoring to barrels - iron is much harder than copper surely?
brinell hardness scale below shows different hardness's of shot materials - if anyone knows what the hardness of your average Damascus barrel is that would be helpful but its very clear why hevishot - steel and tungsten iron are unsuitable.
Edit - Apparently cast iron has a brinell of about ~ 220..
Copper per cartridge is nearly 1/3rd the cost of bismuth - i am sure i could cope with annealing enough for 10 - 15 cartridges if its saving me over £1 per cartridge to do so.
The real answer is to get a gun that shoots steel.
Steel shot can be at at £2.50 /kg - Each cartridge has 0.07 pence of shot in it.
( Graphs from the following link: http://pointingdogblog.blogspot.co.uk/2015/05/pure-copper-shot.html