If you like them, I'd stick with them and just let them know you're going to continue with the meds, but from a different source.
Not sure how the healthcare system works in Sweden, but (an anecdotal example from the U.S.)...I had a specialist who refused to prescribe medicine A unless I took medicine B which gave me horrible side effects and no benefits so I stopped taking it. My grad school program overlapped several courses with Med School, so I've had some pharmacology and knew that her reasoning behind me taking medicine B was BS. Her office was COVERED in swag from the Big pharma company that manufactured med B...I knew what was up: she was getting kickbacks for prescribing medicine B. However, she only found out I wasn't taking med B when my blood tests came back negative for it. (I've dumped her as soon as I was able to as she was shady seven ways 'til Sunday.)
I'm sure with modern healthcare tracking, people who need to know can find out what you're taking via insurance, doc and pharmacy records, but good doctors care more about your health than where you're getting meds.