Well the only time I've ever (unsuccessfully) tried to get UC was at the start of the covid restrictions; it wouldn't have occurred to me not to tell them my job as it made it even more obvious that I couldn't work and had no income.
As far as I know though, it's the amount of money you have coming in that matters and not what your job is (and I think as a self employed person the number of hours you work per week isn't relevant either)? My worry would be that if they find you you lied about the job, they might think you lied about your earnings as well but you have proper documents and an accountant to back that up
I agree that a sex work project with knowledge of this would be ideal, but yes, finding one is going to be hit and miss. Somebody here might have an idea (including one of our project worker members).