Good point, but a number of UN peacekeeping missions have successfully used para-military units, invariably from nations with an armed gendarmerie, first for the occasional public order / riot control duties and when there is a preference for a less military response to situations. Plus the situation may make deploying traditional police officers simply too risky.

A number of European nations have earmarked deployable units, usually the French, Italians and Spanish, for international missions. I exclude SWAT teams. When I looked at this issue a few years ago both Australia (AFP) and Canada (RCMP) had small teams available to deploy.

You are right I cannot think of any Western nation that has:
a force intended to conduct police type operations OUTSIDE their country of origin.