Harry could have had a career in the church, after all he tried being an officer and that didn't work out.
If he is claiming be wasn't trained for anything though, he's a bit of a prat. He was trained to fly apaches. As part of resettlement on leaving the army, he would have been entitled to attend a retraining course - he could have done bricklaying or plastering.
I remember reading an old 'Wills is lazy article and there was a sentence tacked on the end of paragraphs of lambasting William about Harry doing less. His press was always more favourable, he just never realised.