Hi there! I used desensitization training to get my rabbit used to being picked up. It envolves using a clicker(I use my voice) and clicking everytime he does the right behavior and giving food right after so he know the click=food. To desensitize him to it, you start small and click everytime he is calm and lets you touch his side, then both his sides at the same time, then his bum, then his side and bum together at the same time etc. Once he gets use to one motion and stays calm(you must reward only calm behavior) you move onto the next one. And every bun is different, a more skittish bun may take a few months on each stage, and a more confident bun may only take a few weeks, but dont rush it. This does obviously take a lot of time though, so this does not help you for right now, but it may be something you could try after you get his nails clipped.
For his nails, you could try taking him to a rabbit savy vet. Many do nails trims for like $10-15, that way he gets them done and you don’t have to struggle with him.
Hope this helps! I can also further explain the desensitization if you want