Why not check if there's any health conflict with having your first dose of Pfizer and then going through the full process in Geneva, which will most likely be two doses of Moderna.  The reason I say is that the time between requesting a vaccination and getting the appointment here is now pretty quick, only a couple of weeks, so if there's no harm in having had both then perhaps the easiest thing may just be to go through the process in Switzerland.  At least that way you will find it easy to get the certificate and have it recognised in the country you are living.   As soon as you have arranged your health insurance and have your residency here you can make the request.  The alternative would be to keep your second appointment in London and go back for it.  

I reached out to Geneva because I had this issue. I got my first vaccine in the US (moderna). They will not let me get the 2nd vaccine in Geneva and told me that you must get it in the same location as the first one....

I'm traveling back to the US for the second one now. :(

Thanks hucklewoo. I'll enquire if it's medically safe to get 2 doses of the vaccine in Geneva in addition to having had dose 1 already in London. I'm guessing there is not sufficient clinical data on this regimen though, and they will tell me it's not safe to do so.