That honestly makes me upset. I would rather pay the $$ and not sacrifice my passport for another 6-8 weeks (or longer, depending on conditions then), but they should have a way for disabled people to be accommodated. This is an issue with pretty much every immigration related entity, I nearly fainted waiting for my husband's stamp to enter the US thanks to all the people wearing gallons of perfume in the fairly small waiting area.
From my experience at Croydon (2012 and 2014, so it might be different now), you were able to leave the building while waiting. We didn't leave, but there's a shopping centre across the street. I
think they said they could call us when they were ready, but I don't remember for sure since we decided to stay (both were the dead of winter and it was waaaaay too cold outside).
I know that isn't really UKVI making accommodations for your situation and needs, but if you
really wanted to do an in-person application, it
might be an option. It also might have changed since then, so don't make plans based solely on my experience.
If you do make an appointment, try for the first slot of the day and arrive a bit early. That's what we did and it was quiet when we got there, but the crowds came shortly after we'd started the process.