Looking over the list of recent launches, I find communication satellites for countries who do not have their own space program. How many different countries operate a satellite as of 2018? Is that number public?
This list shows all the countries which have, to date, launched satellites - a total of 88. Note that some of these countries no longer exist as a single country (eg. Czechoslovakia), have changed (Soviet Union), are dependencies (Jersey) or are somewhat controversial (Asgardia).
Only 12 countries have natively developed their own launch systems, so all the remaining countries have used foreign or private launch services.
Speculation on non-public launches:
It is very unlikely that any countries have managed to launch orbital payloads in secret on their own due to the obvious problems of trying to hide a rocket launch. However, it seems more possible that a country not on the list has operated a satellite in secret by using a foreign launch provider.