We have plenty of reason to believe these vaccines will be effective with minimal adverse effects (including the relatively small study of 40k individuals).

Conversely, we have definitive proof that in the best case COVID can be asymptomatic and/or a nasty, but survivable, virus. At its worst, it kills you or leaves you with long-lasting health issues that we don't yet fully understand.

Personally, I'll take my chances with the vaccine. My biggest fear isn't adverse reactions, but rather lack of efficacy.

If our best and brightest doctors are opting to get the vaccines for themselves, I feel safe doing the same - it's probably the most clear and obvious signal we're going to get.

All things point to these as being safe, but until it's more widely dispersed I don't think you can assert it as having the same safety as most modern inoculations.

Cautious optimism isn't a bad thing, nor is hesitance to taking the vaccine. Its not really your place to convince them it is safe, that's for them to decide with the facts on hand. Provide them info on the tests, share whatever you have, but it's ok to not trust the speed at which these vaccines were made.