What is a humane disposal of a squirrel?

Having checked on the internet how best to feed the garden inhabitants,was quite surprised to learn feeding grey squirrels in GB is illegal.They are considered to be vermin and one is expected and advised to kill them at every opportunity but do so in a humane manner.Trap and kill or shoot. Well,I cannot not feed them,especially in winter,that would be utterly inhuman when finding food must be so very hard for them,especially the babies.So if any-one wants me to dispose of the grey squirrels that frolic in my garden,they would have to come and do so themselves.