I've been using MyHermes to send fleeces. £5.48 for a big one, £3.78 for one that's less than 2kg .
It's an offence to send faeces by mail, so any fleece being posted or couriered should be skirted, even if it is destined for a compost heap!
The OP's best bet is to ask the local sheep farmer. We all have sacks of daggings and other bits and pieces that we can't include in the wool sheets for the Wool Board, and we'd love to have someone come and take them off our hands!