I finally nabbed him about an hour ago (When he runs away and hides, I like to let him stay hidden and not grab him so that he feels safe in his hiding spaces.). I cleaned up far more poop than I thought possible. His bottom is still dirty. I discovered online that a dry bath using corn starch and a hand vac is the best cleaning solution. So, I ordered those items from Amazon.
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The way I approach rabbits that don't like to be handled is: What needs to get done, gets done, that's a fact, no doubt, no discussion - and no apologies, not even in my mind, well, I do my best. If you are determined in what you are doing this can make things a lot easier, they do pick up if we are insecure, or don't really mean it and put up a fight then.
I always give a treat after doing something the rabbit doesn't like.
It's good to practice that in time, so everyone involved is familiar with the proceedure. I have to brush, pluck and trim the fur of my 10yo Red, she doesn't like to be touched at all, but as she gets older grooming isn't one of her priorities anymore. I have to wear a sweater, winter jacket, sturdy work trousers over my normal ones, she just chews away the second I pick her up, kind of stress relief for her.
But even she doesn't hold a grudge when I'm done, She knows it's over when I put her down, and accepts her little slice of apple.
Imho, corn starch has some use to clean discolourations, like yellow feet on white rabbits, something merely cosmetical and not really much application for that if you don't go to a show.
A hand vac sure comes in handy when it's about cleaning up stray bunny berries, don#t know if there are other uses.
For me the most useful item I have is the pet trimmer. Whatever is stuck to the fur, I usually can cut close to it and get it out.
Good that you have a vet appointment soon, that does sound like there is more going on for some time. A rabbit or it's area starting to stink does ring alarm bells, always a cause to look it over thoroughly.