I sympathise, a lot.
Arthritis means I struggle with cordless chucks sometimes. I have a right-angled drill (Power-Plus: cheap but looks like a DeWalt), and I sometimes have to jam the chuck against it's plastic casing with a wedge as there is no other easy way to stop the back going round. It only gets occasional use, usually DIY, but it's invaluable when I do need it.
I suspect your problem is a bit worse than just removing the chuck of yours.
To start with, it is most likely a left-hand thread, meaning the screw in the bottom of the chuck undoes clockwise. If that screw has a cross-head, it is almost certainly a Phillips profile - don't try a Pozidrive screwdriver as it will almost certainly chew up the head. You need a good quality, long reach Phillips of the correct size (a brand new one would be safest) - those screws are designed to be done up on a production line to a specific torque setting and never undone again. Better tools have Torx and similar screws instead, so you may be in luck.
Then there's finding a replacement chuck - that may be tricky as the keyed variety aren't that popular nowadays for smaller battery power tools. If you can, you're fine, but the manufacturers usually don't intend them to be used in reverse - getting one with the screw hole might be tricky.
And is the thread on the chuck male or female, and what pitch is it? That may not be clear until you have removed it. One thing to consider is that 'one way' chucks (no retaining screw) aren't so good for screwdriving - they come undone when you take screws out. It's not always the case, but it's really annoying if it happens.
But all is not lost, and I'd make a couple of suggestions that might help: First off, you might not have the problem you think you do.
My little 10.8v Bosch drill has a really good clutch, which I think is operated by an electromagnet: It locks the shaft of the drill so that you can open or close the chuck against a rigid shaft. When you squeeze the trigger it unlocks first, then the motor power comes on -- it's so slick you don't really notice. OK, One-handed operation isn't wonderful (grab drill between knees, mutter a bit, etc.), but it's practical.
I've had mine for about five years, and really used it (OK, DIY, but lots). It's still going just fine. If yours is a new drill, and it doesn't work that way, would the supplier let you swap it for one of those models? If you can get one, a simple, rectangular wooden box with shoulders at the bottom for clamps for the bench (or to put one foot on, for DIY) would work: Drop the drill in, chuck uppermost: the box stops it rotating, whilst you undo the chuck with ease.
The other possibility is to contact a Bosch main agent (or the importer), and ask if they can help you. If it's a 'blue' drill it has a warranty that covers contractor usage, and spares will be available. There might be exactly the chuck you need for another Bosch model that they could supply you.
Finally, the keyless sort with a ring at the back (the back cover, really) usually has a plastic cover, moulded into grips. If you can remove the chuck, can you get someone to machine parallel flats in the plastic of the back ring - either slots, or 'rebates' on the back shoulder of the chuck -- which would fit a "C" spanner, probably home made? I could see a wooden frame to hold the drill, chuck uppermost, with a C-spanner, mounted horizontally and sticking out sideways, at the top of it. Clamp the frame to the bench (or put a foot on it if doing DIY) slide the chuck onto the spanner and it can't rotate. Your good hand is free to undo it.
If the above doesn't make sense I'll try to do a drawing. But I wouldn't modify anything unless you're sure you can get a replacement chuck, and do the machining to that so you don't damage the original. Those chucks are designed so they don't need a lot of force to do up tightly, so you shouldn't chew up anythign if the spanner can fit it snugly. You could alternatively mount a strap wrench, as suggested, but it would be slightly more fiddly to use.
Just a few thoughts.
E.