I've always found I need a stable, clean, surface to either inject (MDI) or do a pod change. Many many years ago I did MDI in bathrooms, but trying to balance a vial of insulin, a syringe and (originally) a swab with no safe surface to put any of them on just got too silly, particularly as the ground is generally not carpeted and is instant destruction for a vial of insulin.
I also let the pod control when I change it; I want to get the full 80 hours from each one, so I have a change window of maybe 30 minutes.
Consequently I just do the pod change wherever I happen to be, just as I did insulin injections. Since I am almost invariably with my wife I have a safe surface even in places like airport departure lounges (where the tables are often suspiciously sticky). She just holds the stuff while I fill the pod and plop it on to whichever site is next in my rotation.
When I was working I tended to inject in the stomach, which is quick and easy. When I didn't want to disrobe in a restaurant but wanted to use my upper arm I'd just inject through my shirt.
I don't use my thighs, so I don't have to deal with the inconvenience of wearing trousers. I do always where button up shirts, so it is easy to get to the six sites I routinely use.
Obviously your dress can be an inconvenience. I didn't chose my dress to suit my injection/pod placement needs, I was just fortunate. If I did use my thighs then I would probably chose to adjust my dress on those days where I was expecting to use those sites; while I don't normally wear short-sleeve shirts sometimes I do to facilitate an upper arm pod change.