I don't know about a NEW method, but she wrote an article some years ago that included a few paragraphs with photos on how to trim feet without picking up the foot. Unfortunately, it works best on an animal whose feet are VERY overgrown and twisted. Unless the nail is quite long, you can't get the trimmers beneath the nail to snip it.
I've used this method before on a male I used to have that would freak when I tried to do his nails. He's was okay with it because I wasn't touching him to do it. It worked quite well, but you can't get a very close cut this way. It's much better to train them to let you handle them but if you have an alpaca that just won't tolerate being handled, cutting their nails while they are standing is less stressful for you and them.