Hi Amanda,
I know exactly what you mean, so just know that you’re not alone! Thor hates being picked up, and this is normal for rabbits. Your rabbits are still young, so you just need time to bond with them, and I think this is how a rabbit willingly allows you to clip their nails, no matter the technique. I only just learnt how to cut Thor’s nails by myself without picking him up like the professionals do. Let me just tell you that it took me many months to feel comfortable picking him up in general (and not feeling awful about it), and even longer to actually cut his nails myself.
For now, I would recommend you get their nails cut by the vet or a rescue, just till you build confidence to do it yourself. Yes, it will cost $$ but I never regretted paying someone else, because it bought me time and reduced my stress. And you don’t want their nails to get snagged on anything.
I could give you steps on how to nail trim, but I think the most helpful thing is petting and grooming a rabbit regularly. You gotta do a lot of ground work, which equates to allowing them to approach you, bribing them with treats, petting them everyday, and just plain ‘ol patience. You are right, you never want to wrestle with a rabbit to do anything they don’t want to (other than giving meds!). Of course, you will have to pick them up now and then so just stay positive and confident. Bunnies sometimes behave like they want nothing to do with you, but we’ve all had to deal with this, so we just soldier on, and do what we know we need to do to keep them healthy.
You can start out by interacting with them on ground level. As they allow you after some weeks or months of consistent interaction, you can move them to a towel on a washing machine/ dryer to clip nails or brush them during a heavy shed. It doesn’t have to be a perfect lift, but just hold them firmly enough (always suporting bum/ spine) so you can get them safely from point A to point B. Rabbits can sense uncertainty, so they will exploit the moment by trying to escape.
Despite the fact that Thor hates being picked up, he allowed me to manoeuvre him this way and that during nail trimming, because it is how I interact with him when I groom him. It was easier than I thought. He knows when I gently lift his front paws and body forward together – grooming, treats and ear rubs will usually follow. I think if a rabbit primarily associates touch with being picked up, they will probably run or lash out, but when they learn that mainly good stuff comes out of the deal, they are more easily coerced. I give tiny treats after each nail is trimmed to create positive associations. I also do this with extended grooming sessions, and it works well for both rabbits.
Sorry for such a monstrous reply (I don’t do “concise” very well), but I forgot to mention that I never have to turn Thor over, etc when I do anything. His paws stay planted on the surface I place him on, and he let’s me gently ruffle him about during clipping and grooming.