I think it’s fine, it’s a routine screening only service offered to all women in a certain age group, so it doesn’t reveal anything about you - other than that you’re sensible enough to want screening. Our service has always been provided in a mobile unit here, it travels to different areas every week so it is easiest for local women to access.
It wouldn’t bother me personally if I needed chemotherapy in a mobile unit either, because I think if I was feeling really unwell I’d rather be as short a distance from home as possible, and that would override any embarrassment.