Additionally, perhaps you are better equipped than I to know, but I believe you could control for any risk you perceive (which I think is ridiculous, but to each his own) from having someone inexperienced administering the vaccine by getting it from your GP.
As for the transmission of COVID-19, if you require absolute proof that vaccination will prevent all transmission then you are setting your bar far too high and your position is indefensible.
To start the presumption is that it is very likely that vaccination will at the very least reduce the likelihood of transmission because while there are viruses like Measles that can still be transmitted in such circumstances those cases are the exception to begin with.
Furthermore evidence is building that vaccination against COVID-19 prevents people from carrying loads of the virus that can be transmitted, if you are quite as committed to this line of argument as you seem to be I am sure you can find the published and pre-pub studies out there. I am confident that if you went about booking yourself an appointment for a month from now by the time your appointment were actually up you'd have lots more evidence to avail yourself of - and you'd always have the option of declining at the time!