@finswimmer, thank you for your answer.
I was aware of the dbsnp endpoint from Exac's REST-API, but ruled it out as an option since it can handle only one dbSNP per query at a time. For my immediate task, I have ~70k such ids, and in the future I expect to deal with even larger numbers of them. I estimated (perhaps incorrectly) that a solution involving ~70k HTTP requests would be both slow on my end, and perhaps be not appreciated by the administrators server-side.
The second API you mentioned I had not considered at all, but it too can handle only one dbSNP per query.
I will investigate further to see if I can get this approach to work in a reasonable time.