I know that some tests now are mouth swabs, which certainly seems more palatable. Not sure if there's a difference in accuracy.
As a veteran of head and neck cancer I've had most of the ENT's repertoire of torture devices inserted into my nose, notably the nasal endoscope, which is a long black rubber tube with camera and light at the end that goes in, in, in, and up, up, up and then down, down, down. And plenty of regular endoscopes and the like. What can I say: they're unpleasant but you do get used to them. (and I'd certainly trade the experience for a DRE... but will take the sinus journey any day over another cytoscopy)
That said, when I had my county COVID test at the end of March it was still being done by oral swab. I later learned that those are notoriously unreliable as the virus is much more concentrated in the sinuses. So my negative on that might well have been incorrect. The nasal swab, as uncomfortable as it is (the medicos never use the word painful for these things; don't want to scare the prey) is a much better bet.
Let's hope people only have to do it once!